M. Abdel-Naby, H. F. Ragaie, and F. El Akkad. Abstract-Capacitance-voltage and conductance-voltage characteristics of RF-sputtered ZnCdS films on ZnTe ...
IEEE TRAI\ISACIIONS O b FLECTRON DEVICES. VOL 40. NO 2. FEBRUARY 1993
Capacitance and Conductance of ZnxCdl S/ZnTe Heterojunctions -
Abdelhalim Zekry. M . Abdel-Naby, H . F. Ragaie, and F. El Akkad
Abstract-Capacitance-voltage and conductance-voltage characteristics of RF-sputtered ZnCdS films on ZnTe single crystals were studied as a function of frequency up to 1 MHz. It has been found that the measured capacitance decreases with frequency while the conductance increases. A physical circuit model of the junction is proposed which can explain satisfactorily this dependence. We derived a relationship relating the junction capacitance to the polycrystalline film properties and the built-in voltage of the junction. One of the main results of this relationship is that the junction capacitance is related to the average carrier concentration rather than the doping concentration of the polycrystalline material. From a C versus V plot we obtained an average carrier concentration in the films which is in good agreement with that obtained by Hall measurement. The lower merage electron concentration in the ZnCdS film near the substrate is due to either interdiffusion of Cd from the film into substrate or due to higher density of grain boundary states in the starting deposition portion of the film.
the characterization of these junctions, small-signal capacitance-voltage and conductance-voltage measurements have been performed at different frequencies. From this study we determined the effective carrier concentration in the polycrystalline film and the built-in voltage of the junction. This is useful for enhancing the performance of such junctions in solar cell applications. It is also believed that the influence of Zn concentration in Zn, Cd, p , S film on the properties of the interface layers is not fully explored. In an earlier publication  we reported that due to the rapid increase in the resistivity of undoped RF-sputtered Zn, Cd, . S films with increasing Zn concentration x, the range of usable composition for solar cell applications is limited to values of x smaller than 0.2. Therefore, this study will be restricted to x 6 0.2.
I. INTRODIJCTION ECENT STUDIES [ I ] ,  have been conducted on CdS /ZnTe heterojunctions for the realization of stable and low-cost solar cells. A preliminary investigation of the CdS/ZnTe junction was reported by Aven and Cook 131. Subsequently, the system was studied by a number of research groups , [ 5 ] . However, the ma.jority of the work already conducted was devoted to the electrical properties of the junction with emphasis on the minority-carrier injection mechanism because of its importance for electroluminescence applications. Recently, Kimmerle et al. [ I ] replaced CdS with a mixed sulphide layer Zn, Cd, ,S in order to improve the photovoltaic conversion efficiency of such junctions. In a previous paper , it was found that the current follows the relation: I = Io exp V / n V , . with I Z the ideality factor and Io the reverse saturation current. The ideality factor IZ is about two and I,, amounts to 5 x l o p 6A. The current conduction in such junctions is dominated by recombination at the interface. For specimens with 0.05 zinc concentration the series resistance amounts to 140 Q . cm' and the shunt conductance is approximately few millisiemens per square centimeter. The value of the built-in potential was determined to be 0.65 V. I n order to complete
For heterojunction formation, ZnTe single-crystal p-type, phosphorus-doped wafers of 0.5-mm thickness and doping concentration of 4.4 x lOI7/cm' were mechanically polished. They were then chemically etched in brome-methanol solution for 3 min to remove the mechanical damage from the surface layer. Finally, the wafers were cleaned in pure methanol then rinsed in distilled water and dried by a flow of N2 prior to loading into the sputtering chamber for deposition. The polycrystalline Zn, Cdl -.r S films were RF-sputtered from hot-pressed targets of variable Zn content x (x = 0.05 and 0.2). The deposition temperature wts 220°C and the deposition rate was adjusted to about 5 A / s under a vacuum of about 2 x torr. The deposited film thjckness was about 1 pm. The grain size amounts to 400 A . Ohmic contacts to the ZnrCdl films were obtained by evaporating an indium layer ,  of about 0.5-pm thickness under a vacuum of about IO-' torr, while ohmic contacts to ZnTe were obtained using chemically deposited Au. C- V and G- V measurements at 1 MHz were made using an E.G.&G. model 410 C-V plotter. At lower frequencies, the same measurements were carried out using an HP model 427A multi-frequency LCR bridge.
Manuscript received May 7, 1990. revised August 30. 1991 and July 21. 1992. The revieh of this paper was arranged by Associate Editor S . J . Fonaah. The authors are with the Electrical Engineering Ikpartment. King Saud University. P . O . Box 800, Riyadh 11421, Saudi Arabia. IEEE Log Number 0205 166.
Fig. 1 shows the measured junction capacitance as a function of the reverse-bias voltage V fur a Zn, Cd, ~.,S/ZnTe diode with x = 0.05, at different fre-
111. EXPEKIMENI A L RESULTS
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 40, NO. 2, FEBRUARY 1993
I :U) KHz
0 I =loOKHz
I .LO KHz I z I HHz I
Fig. 1. Typical C-Vcharacteristics of Zn, ,Jd, quencies.
&/ZnTe at different fre-
quencies ranging from 10 kHz to 1 MHz. The rate of decrease of the junction capacitance with the reverse bias is more pronounced for V ,< 0.5 V. At higher reverse-bias voltages, the capacitance decrease slows down. Consequently, the width of the junction depletion layer increases with the reverse voltage. In contrast, Fig. 2 shows that the capacitance of a junction with x = 0.2 is nearly independent of the applied reverse bias. Therefore, the junction depletion region fills the whole film thickness at thermal equilibrium. It is also obvious from Figs. 1 and 2 that the capacitance of the two specimens decreases with frequency. The average electron concentration n, in the film was measured using the Hall effect and calculated from the relation [l 11 n, = 1 / e R , where R is the Hall coefficient and e the electronic charge. It amounts to 5 X 10I6/cm3 for x = 0.05 and to 10i5/cm3 for x = 0.2. Since the average carrier concentration in the film is much smaller than that in the ZnTe substrate, the junction space-charge region extends mainly into the film material. Consequently, by plotting l / C 2 versus the reverse voltage we can determine the average carrier concentration in the film and its variation with the distance from the interface. This was only possible for the specimen with x = 0.05. Fig. 3 shows 1 / C 2 against the reverse-bias voltage for this specimen at different frequencies. It is clear from this figure that the ( C P 2 - V )relation is generally nonlinear. However, each curve can be fitted approximately with a broken line consisting of two linear portions. For fixed frequency, the slope of the straight line at higher voltages is smaller than that of the straight line at lower voltages. In addition, the slopes of all the straight lines increase with frequency. The interception of the lower voltage straight lines with the voltage axis would result in different values for the built-in voltage. Therefore, we can extract the average camer concentration and the built-in voltage of the junction from these ( C - 2 - V ) plots. At low frequencies, one can ideally determine an approximation
Fig. 2 . Typical C-V characteristics of Zn, zCdo ,S/ZnTe at different frequencies.
for the average carrier concentration from the local slope at any point on the 1/ C 2 versus V curve, even though the barrier height cannot be determined by straightforward extrapolation. These parameters will be extracted in the next section. Figs. 4 and 5 show the small-signal conductance as a function of reverse voltage at different frequencies for x = 0.05 and x = 0.2, respectively. It is seen from these figures that the conductance of both samples increases with frequency. The conductance of the specimen with x = 0.05 decreases with voltage while that of the other specimen with x = 0.2 increases. This behavior of the conductance will be explained in the next sections. IV. THEORETICAL MODELS A . Junction Capacitance of Heterojunctions from Polycrystalline Material We now derive an expression relating the junction capacitance CJ with the bias voltage V across it. To our knowledge such an expression has not yet been derived in the literature. Fig. 6 shows a schematic diagram of a one-dimensional polycrystalline heterojunction. The right side of the junction is n-type while the left side is p-type and the transition at the metallurgical boundary is abrupt. Let us assume that each material consists of identical grains with grain size equal to the average grain size 1, of the actual material. The grain size of the n-type material is lgnand that of the p-material is fg,. The doping concentrations are NA and No in the p- and n-type materials, respectively. It is known that a space-charge region around the metallurgical junction will be formed to absorb the overall potential difference between the neutral n and p sides. The widths of the space-charge regions are W, and W,, in the p- and n-type materials, respectively. The problem is now the determination of W, and W, as a function of the potential difference across the space-
CAPACITANCE A N D CONDUCTANCF OF ZnCdSIZnTe HETFROJUNC I l O N S
00 -4 5
Voltage ( V o l t )
Fig. 3 . Typical C ' - V characteristics of Zn,, ,liCd,,,,,S/ZnTe at different frequencies
- - ------LWP-4-W"
+ + + + + + + + + +
Fig. 6 . Schematic diagram of one-dlmenaional polycrystalline heterojunction.
Fig. 4. Typical G-V characteristics of Zn,, &d,, ,,S/ZnTe frequencies.
Fig. 5 . Typical G-V characteristics of Zn, ,Cd,, ,S/ZnTe at difkrenl frequencies.
charge region. Starting with the space-charge distribution one can get the electric-field distribution and the potential distribution V ( u ) . Because of majority-carrier trapping at the grain boundaries a space-charge region will be formed around each grain boundary according to the Seto model [SI for a polycrystalline material. Let us denote the width of the space charge associated with each grain boundary by W,,, in the n material and W,y,, in the p material. This width depends on the occupied trap density Q, in the grain boundary and the majority-carrier concentration inside the crystallites. Assuming that the traps are homogeneously distributed in the energy gap, the occupied trap density, e.g., Qrf,,in the p side is proportional to the energy difference AE,, between the Fermi level Er,, and the conduction band edge E , . This energy difference decreases in the transition region from (E,y - Et,,) in the neutral p side to (E,? - Et,, - e$,,) at the metallurgical boundary of the heterojunction where $,, is the built-in voltage in the p side. Typical values for our heterojunction are EI: = 2.26 eV. E,,, = 0.2-0.3 eV, and $/, = 0.3 V. Therefore, A E , varies from 2 to 1.7 eV in the p side of the transition region. We have to mention that this model does not take into account that, in most semiconductors, the trap distributions may be highly peaked at various energy positions in the bandgap and, as a result, it is normal in at least some of the 11-VI compounds, to see the grain boundary barrier potentials pinned at a particular value. Any movement of the Fermi level is then resisted by large changes
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 40, NO. 2, FEBRUARY 1993
in the trap charge density. In addition, one has to consider the effect of grain boundaries perpendicular to the juncchanges only by about 15% tion plane. Consequently, in the whole transition region. The same holds for the transition region on the n side. Therefore, one can assume that Qrpand Q,, are nearly independent of position in the transition region. This serves also to simplify the mathematics. For fine-grained polycrystalline material and large average grain boundary states, as is the case for our sputtered material at low temperature, our assumption of constant Q, throughout the depletion region will be strictly valid since there are always more trapping states than the total free carriers inside the grains. Consequently, the space-charge distribution in a polycrystalline heterojunction is shown in Fig. 7 assuming that the ionized dopant concentration is independent of x. Q,, is the interface charge. The number of depleted grains in the p material is y,,and that of depleted grains in the n material is y,,. The electric field distribution E,, (x) in the space-charge region of the p material can be obtained using Poisson's equation in one dimension, i.e.,
where D,, is the electric displacement and p,, is the charge density in the p material at point x. Assuming that the space charge ends in the neutral por( - W,,) = 0. The distion of a grain, the displacement D,, placement D,, (x) can then be found by integrating ( 1 ) from x = - W,, to a general point (-x) i.e., P
Fig. 7. Schematic charge distribution.
Fig. 8. Electric field distribution in a polycrystalline heterojunction. The inset shows the electric field distribution of the space charge due to grain boundary.
We want to determine the potential at the metallurgical boundary where x = 0. Therefore, one has to calculate the area under E,,(x) from - W,, to x = 0. Hence
But we have
The left-hand side of (2) is equal to the area under the space-charge distribution from x = - W,, to -x. Therefore, the magnitude of D,, increases linearly with a slope = eNA, inside the grain bulk till it reaches the grain boundary where it drops abruptly. The magnitude of the is the trap charge inside the drop equals Q, where grain boundary. Inside the grain bulk, the magnitude of Dp increases by eNA1,. Dividing D,, by E,, we obtain the electric field distribution E,,@) shown in Fig. 8. The electric field E , , ( x ) of the space charge due to a grain boundary alone is shown in the inset of Fig. 8 and by the dashed line in the overall field distribution. The total width of the space-charge region due to grain boundary is denoted by WRp.Due to symmetry, the grain boundary lies in the middle of W,,, such that the area under the ERh(x)is zero. Now, the potential distribution on the p side can be deas a reftermined. Taking the potential V ( x ) at x = erence to zero value, V ( x ) can be found using the expression --I
V(x) = - WP
Substituting ( 5 ) in (4)we get
2V(O) = ( 1
1) = 7;.
With y P l ,
W,,, (6) reduces to
21/(0) = ( i
Equation (7) becomes identical to that of a single-crystends to zero. We notice also for talline material if Wg,, the same potential difference V ( 0 )across the space-charge region on the p side the polycrystalline material has a larger space-charge width than the corresponding monocrystalline material with the same doping concentration N A . The correction factor amounts to (1 - Wg,,/1,,,). From the neutrality condition we get
Q, w&,, =
ZEKRY er ul
CAPACITANCE AND CONDUCTANCE OF LnCdS(7nTs HETEROJUNCTIONS
where Q,, is the positively charged trap density at a grain boundary. A similar expression holds for the space-charge region on the n side, i.e.,
where V (W,,)is the potential at x = W,,,E , , is the dielectric constant of the n material, and WqIlis the space-charge width due to traps at the grain boundary in the n material. Because of neutrality Whl,can be expressed by the relation
where Q,,, is the negatively charged trap density in the grain boundary of the n material. From the neutrality of the whole transition region we get the relationship between W,, and W!);i.e.,
Combining (7), (8), and ( 1 1) we obtain the required expressions for the widths W,, and W,, of the transition region as a function of the potential difference V(W,,) across it I 05
Combining (14) and (15) one obtains
It must be mentioned that this result can be formally obtained by directly modifying the ionized doping concentration No of a monocrystalline material to account for the trapping of electrons at the grain boundary. The trapped electrons can be considered as if they were homogeneously distributed acceptors with a concentration Ni = Q r t l / f g ~ i . It is clear from (16) that CJ decreases as the ratio W,,,/I,,, increases. ( A / C , ) ’ will be multiplied by the factor 1 / ( I - W ~ , , / l ~ ,which ,) can be much greater than unity. The determination of the ionized doping concentration neglecting the effect of grain boundaries can result in a much lower value than that actually present. Expressed in terms of the slope of 1 / C J versus V , one can determine only some average ionized dopant concentration 12,. given by
which can be much smaller than the doping concentration No inside the grains. Physically. n,, represents the average equilibrium concentration of the remaining electrons inside grains after trapping a fraction of them. As before, the intercept of 1 / C; versus V with the voltage axis gives the built-in voltage 4 of the junction provided that the ionized dopant density is constant throughout the entire depletion layer.
B. Deptwdcnce of the Junction Capaciranre and Conductance on the Frequency (13) The potential difference V ( W,,) depends on the biasing of the junction. So, it is equal to the contact difference of potential 4 in case of no bias while it amounts to 4 7 V in case of forward and reverse biasing. respectively. For unsymmetrical junction such that NA >> N, as in our case, Wp will be