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Electron and hole injection by a metal-depletion layer contact
Solid-State
Electronics
Pergamon
Press 1964. Vol. 7, pp. 225-235.
Printed in Great Britain
ELECTRON AND HOLE INJECTION BY A METALDEPLETION LAYER CONTACT* P. G. SEDLEWICZt, Electrical
Engineering (Received
R. E. ONLEYI
Department 20 August
and
Northwestern
1963
; in rewisedform
C. R. KANNEWURF University,
Evanston,
14 October
Illinois
1963)
Abstract-The injection of electrons and holes by various metal probes into the depletion region of a beveled silicon p-n diode was experimentally studied. The electrical and thermal properties of metal pressure contacts are presented and used to identify the nature of the injection mechanism. The characteristics of electron injection are shown to be of the space-charge-limited type and the hole injection characteristics follow a high field process. A potential energy diagram of the metaldepletion layer contact is presented and appears to be in agreement with the observed injection phenomena. RBsumC-L’injection d’6lectrons et trous par diverses sondes mt%alliques dans la rCgion d’kpuisement d’une diode au silicium biseautee a CtC BtudiCe expkrimentalement. Les propri&Cs Clectriques et thermiques des contacts & pression de m&al sent prCsentCes et employees g identifier la nature du mkcanisme d’injection. Les CaractCristiques de l’injection d’klectrons sent dCmontrCes comme &ant du type & charge d’espace limit&e et les CaractCristiques d’injection des trous suivent un pro&d& de champ blev& Un schema d’Cnergie potentielle du contact de la couche d’epuisement est pr&entC et semble &tre en accord avec la phCnom&e d’injection obserd. Zusammenfassung-Die Injektion von Elektronen und LBchern mit Hilfe verschiedener Metallsonden in die Sperrschicht einer abgeschrlgten Silizium-p-n-Diode wurde experimentell untersucht. Die elektrischen und thermischen Eigenschaften metallischer Druckkontakte werden dargestellt und dienen zur AufklLrung des Injektonsmechanismus. Die Kennlinien fiir Elektroneninjektion zeigen einen durch Raumladung begrenzten Strom, die fiir die Lccherinjektion eine Emission nach Schottky. Ein Diagramm der potentiellen Energie des Kontaktes zwischen Metal1 und Sperrschicht wird angegeben; es scheint mit den beobachteten Injektionserscheinungen iibereinzustimmen.
1. INTRODUCTION
presented the “spacistor”, a high frequency transistor also using contacts in the depletion the depletion region of a reverse biased p-n wafer region. These groups investigated the two-port parameters of the device and discussed injection was first reported by PEARSON, READ and SHOCKLEY.(~) Following this work MATTHEI and only from a qualitative point of view. LAVINE, BRAND,(~) and GiiRTNERt3) developed high freRINDER, NOST and NELSON,(~) continued the work quency transistors using an injection contact in the with the “spacistor”. LAVINE(~~~) developed a depletion region. STATZ, PUCEL and LANZA@) device with n- and p-doped contacts within the depletion region and made an analysis, which * This work was supported in part by the U.S. Navy predicted the current to be space-charge-limited. Bureau of Weapons, Contract NOW 62-0749-d. This paper is a portion of a thesis submitted by P. G. SedleThe experimental investigation presented here wicz in partial fulfilment of the requirements for the describes the electron and hole injection characterdegree of Master of Science at Northwestern University. istics of various metal pressure contacts within the 7 Present address: hp Associates, Palo Alto, Calidepletion region of beveled p-n silicon wafers. fornia. In addition to the electrical properties of injection, $ Aerial Measurements Laboratory, Northwestern some thermal properties are also discussed. University. THE injection
3
of carriers
from
a metal
contact
into
225
226
P.
2. PREPARATION
G.
SEDLEWICZ,
OF SAMPLES
AND
R. E. ONLEY
and
C.
R.
KANNEWURF
PROBES
In order to investigate the injection of carriers into the depletion region, a wide depletion region at the surface of the sample is desirable. Standard p-n silicon discs were formed by a deep diffusion of acceptors from a constant surface type concentration.* The p-n discs were 10 mils thick, 0.75 in. dia. and had gold plated electrodes on both sides. The n-type substrate was high resistivity material, 100 Q-cm or greater. In order to obtain a wide depletion region at the surface, the p-n discs were beveled across the junction at angles between 1 and 2”, polished, and then etched in a standard CP-4 solution. The metals tungsten, aluminum, gold, zinc and cadmium were selected for the probe materials because they could be worked to a fine point and could withstand the force necessary to achieve a good pressure contact. Also, these metals have reasonably different work functions. Most of the tests were made with the tungsten probe because of its somewhat more durable point. 3. EXPERIMENTAL ARRANGEMENT The electrical connection to the p-side of the beveled p-n wafer was made by soft soldering the wafer to a brass disc which was mounted on the bed of a Wilder probing stage. A pressure contact was used to make the electrical connection to the gold plated n-side of the p-n wafer. A pivot arm was positioned over the bed of the stage so that the various metal probes could be accurately positioned in the depletion region. Figure 1 is a pictorial diagram of the experimental arrangement. Relative dimensions of the depletion region and angle of the bevel have been exaggerated in the diagram for clarity. With an angle of 2” the movement of the depletion region on the surface will be geometrically increased approximately 30 times that of the bulk movement. The curvature of the depletion region at the surface was discussed by LAVINE(~)and it has been experimentally determined to be very slight. This indicates that the major increase at the surface of the depletion region is determined geometrically. Since the resistivity of the n-side of the junction is several orders of magnitude greater than that of the p-side, the movement of the depletion region * The p-n discs were donated by Hoffman Electronics Company, Evanston, Illinois.
FIG.
1. Metal-depletion
layer
injection
arrangement.
can be considered to be entirely into the n-material. One electrical circuit was employed to reverse bias the beveled p-n wafer and another to apply various potentials to the metal probe. The microammeters, In and I,, read the leakage current through the p-n diode when the probe circuit is open. With the probe connected to a high impedance voltmeter, the potential distribution on the beveled surface can be determined and the probe can be located within the depletion region at any floating potential, V~O.The floating potential is defined as the potential of any point within the depletion region relative to the p-side of the wafer. When the probe is biased positively with respect to the floating potential, holes are injected; the high field within the depletion region sweeps the holes to the p-side of the wafer; and the injection current, indicated by microammeter If, adds to the leakage current 1,, while In remains constant. When the probe is biased negatively with respect to the floating potential, electrons are injected; the field sweeps the electrons to the n-side of the wafer; and the current lr adds to the leakage current In, while 1, remains constant. Distortion of the depletion region by a metal pressure contact, which causes irregularities in the injection current, was minimized by using contacts with a diameter of two mils or less. The pressure applied to the metal point contact was varied from 6 x 10s to 3 x 1010 dynes per ems. There were no changes in the injection characteristics due to this pressure variation only.
ELECTRON
AND
4. ELECTRON
HOLE
AND
HOLE
INJECTION
BY A METAL-DEPLETION
INJECTION
I
CONTACT
227
probe potential for all values of voltage greater than the floating potential at the probe point. The same general characteristics were obtained from a number of samples of which two typical curves are shown in Figure 4. Variations in the magnitude of
Figure 2 shows electron injection with tungsten probes, where the voltage, V,, is the probe potential for all values of voltage less than the floating potential at the contact point. The two
102_
LAYER
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.8 TUNGSTEN
PROBE .-
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FIG. 2. Electron injection for the tungsten probe (V,
curves shown are typical for all samples and for various probe positions. In most cases samples were reverse biased at 115 V and the probe was positioned at a floating potential of approximately 55 V. The curves are seen to have the same slope but are separated by an order of magnitude, which is generally the range covered with the samples investigated. Typical electron injection curves for the Al, Au, and Zn probes are shown in Fig. 3. Figure 4 shows a plot of hole injection for a 1 mil tungsten probe where the voltage, VP, is the
IO2 < Vfo).
the injection current and in the slope of the linear region were observed. The hole injection curves showed a very rapid initial increase, then a transition region, followed by a constant slope over several orders of magnitude. The magnitude of the hole injection current was always less than that of the electron injection current where 1VP1 = 1J&l. Hole injection for the Au, Al, Zn, and Cd probes is shown in Fig. 5. A comparison of the various graphical representations for hole and electron injection data will be given in Section 6.
P. G. SEDLEWICZ,
228
R. E. ONLEY
and C. R. KANNEWURF
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ELECTRON
in
AND HOLE INJECTION
BY A METAL-DEPLETION
LAYER CONTACT
229
injection curves. Hole injection for the tungsten probe was stable except at low temperatures where breakdown was observed. This may be attributed to the presence of moisture on the surface of the sample. This series of curves shows an increase in injection current and a decrease in the slope, with increasing temperature. Although not presented here, similar results to that of Al and W were also obtained for both electron and hole injection as a function of temperature with gold probes in the depletion region.
‘o’r----J
E IO0
0 i
6. DISCUSSION a. Contact model The experimental data presented in Sections 4 and 5 show the electron injection characteristics of a metal-depletion layer contact to be different from those of hole injection. Electron injection exhibits a linear relationship when plotted as log Ivs. log V, whereas hole injection exhibits a linear relationship when plotted as log I vs. VI/s; o Zn probe also the temperature dependence of electron A Al probe injection is different from that of hole injection. + Cd probe LAVINEt7) has discussed the characteristics of nv Au probe and p-doped contacts in a depletion region and has described potential energy diagrams for these contacts. A potential energy diagram of a metalg lo ’ ’ depletion layer contact and its relation to hole and I B electron injection will now be discussed. (volts) In the depletion region mobile electrons and FIG. 5. Hole injection for the Zn, Al, Cd, and Au probes holes have been removed by the high field leaving (VP > vfo). a space charge of donor and acceptor ions. SAH, NOYCE and SHOCKLEY@)have investigated the 5. INJECTION AS A FUNCTION OF location of the quasi-Fermi levels within the TEMPERATURE depletion region. They describe the potential Injection as a function of temperature was in- diagram within the depletion region and show the potential gradient, valence and conduction vestigated for the W, Al, and Au probes. Measurements were made in a temperature range from bands, a quasi-Fermi level for electrons, & and a level for holes, &. The relationship -50 to +lOO”C. Figures 6 and 7 show the quasi-Fermi between the carrier concentrations and the electron injection curves for the W and Al probes levels can be exwith temperature as a parameter. Electron in- positions of the quasi-Fermi pressed as follows: jection for the tungsten probe showed very little variation with temperature except below room n = nc expp(‘n-flr) (1) temperature. The final slope of the injection kT current did not change over the temperature range investigated. (2) Figures 8 and 9 show hole injection for the W and Al probes respectively with temperature as a where (& - #) represents the separation in potential parameter. The hole injection data were taken under the same conditions as those for the electron between & and the mid-gap position. Equations
VPF
230
P. G. SEDLEWICZ,
R. E.
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(SduD”)
II
ONLEY
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and
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“0-
ELECTRON
AND HOLE
INJECTION
BY A METAL-DEPLETION
LAYER
5 i 5 &J 2 Z $ F 2 $ W
p
231
as 4kT/q units below mid-gap and to extend to 12kT/q units below mid-gap and I+$, to have a similar range above mid-gap. In the depletion region the valence band will TUNGSTEN PROBE be partially empty, a fixed number of ionized donors and acceptors will be present, and a space 10’ charge of electrons will be established. Figure 10 shows the proposed metal-depletion layer contact. In the vicinity of the probe all effects due to surface states and oxide contamination layers have been neglected. It is assumed that the extent of too the depletion region is small enough that the potential gradient need not be shown. The location of the Fermi level, &, for the various metal probes relative to the valence and conduction bands (as shown in Figure 10) will id’ now be considered. Measurements of the forward and reverse V-I characteristics for the various probes positioned in the n-type region indicated the contacts to be ohmic in all cases. Therefore the Fermi level for these various metals must lie between mid-gap and the conduction band. Since lo-2 this is a high resistivity n-type material, the Fermi level of the neutral material must be several kT/q units above mid-gap. The position of the Fermi level of the metal has now been located relative to the quasi-Fermi levels within 10-3 8 9 IO I I the depletion region. Before contact is made 0 I 2 34567 I I between the metal and the depletion region, the (“01 t Fermi level of the metal is very close to the quasiP Fermi level for holes. When contact is made FIG. 8. Hole injection for the tungsten probe with temperature as a parameter. the Fermi energy levels in equilibrium must be at the same energy level, which requires the Fermi level of the metal to align itself with the quasi(1) and (2) can be used to define the shift of the quasi-Fermi levels from the mid-gap positions as Fermi levels, C& and &,. The location of the quasiFermi level, &,, can be considered, for simplicity, follows : to be approximately the same as &. This locates kT n A+, = -ln& between SkT/q units and 24kTlq units below (3) ni Q &. The level, &, can align itself with & and & if a space charge of electrons exists in the conA+, = krln?. duction band at the interface. Electrons from the 4 P metal can establish this space charge and the The location of A& and A&, on a potential energy magnitude can be approximated, as discussed by diagram will be determined by n and p. Since the MOTT and &mm-,(~) by the following equation : concentration of electrons and holes in the space charge region is much less than nt, the intrinsic exp - q($m - 44 (5) concentration, & will be located below the midkT gap and & will be located above mid-gap. SAH et al.(s) have estimated the range for A+, and where q(&--&) is the energy difference between A&. These estimates have shown cjn to be as close the Fermi level of the metal and the quasi-Fermi IO2
‘;; a.
CONTACT
VT
2
312
232
P. G. SEDLEWICZ,
R.
E.
ONLEY
and
C.
R.
KANNEWURF
FIG. 9. Hole injection for the aluminum probe with temperature as a parameter.
level for electrons. In view of the preceding discussion this can be considered equal to 2A4,. Using the value of A$, given by SAH et al.,@) No can vary from 3 x 1011 to 3 x 101s electrons per cm3 at the interface. b. Electron Injection The characteristics of the depletion region are to some degree more like those of an insulator than of a semiconductor. There are a negligible number of mobile carriers and a fixed space charge is established. MOTT and GURNEY(~)showed that an insulator without mobile carriers can maintain a current if electrons are raised into an energy band that is normally empty. Electrons can be thermally excited from the metal contact to the conduction band of the insulator if the energy gap is much less
than 1 eV. For this situation the dependence of the current on the voltage is said to be spacecharge-limited and Mott and Gurney give the following equation for the current density:
where L is the thickness of the sample. Recently, several authors have extended Mott and Gurney’s work to include the effects of traps, surface barriers, and lattice defects.(lsJr) ROSE has shown that the V-I characteristics in cadmium sulfide initially follow an Ohm’s law relationship and then make a transition to a region of spacecharge-limited current. It will now be shown that the experimental data for electron injection follow a space-charge-limited relationship.
ELECTRON f $
Electron
AND
HOLE
INJECTION
BY A METAL-DEPLETION
+Metal
I
Depletion
Region
-w
energy diagram of the metal-depletion layer contact.
Electron injection is shown in Figs 2 and 3 on a log-log plot. As the injection voltage increases, the curve makes a transition to a linear region with a slope of approximately 2. This type of behavior can be identified with a space-charge-limited current. Some variation in the slope of the linear region from the ideal slope of 2-O was found to occur; ROSE observed a similar type of variation in cadmium sulfide which was attributed to nonohmic contacts. The onset of the region also varied from probe to probe and from sample to sample. This can be related to changes in the barrier height at the interface. The final slope for the various metal probes is tabulated in Table 1. Table
CONTACT
233
however, that for the various probes the initial slope was approximately unity, which is characteristic of space-charge-limited current at low voltages. The total space charge should not vary with temperature but the fraction of the charge which is free for conduction should increase exponentially.(la) Therefore the electron injection curves should translate with temperature. This was investigated for electron injection and is shown in Figs 6 and 7. The slope of the injection curves for all the various probes was maintained throughout the temperature range tested.
Potential
FIG. 10. Potential
LAYER
1. Slope of electron injection curves
Probe
Slope (average values)
Tungsten
2.0
45
Zinc Gold Aluminum
1.9 1.7 1.9
12 10 9
Number
-
of trials
The initial slope of electron injection was not tabulated because of the greater experimental errors at the low voltages. It was observed,
c. Hole injection The mechanism for electron injection cannot be applied to hole injection for the metal-depletion layer contact. Electron injection, which has been identified as a space-charge-limited process, requires an ohmic contact, the existence of a space charge region, and a small energy gap between the Fermi level of the metal and the conduction band. Hole injection exhibits none of these characteristics. The model presented for the metal-depletion layer contact shows a partially filled valence band, a large energy gap between the valence band and the Fermi level of the metal, and no space-charge region of holes. The injection of holes by a metal-depletion layer contact can be accomplished by removing electrons from the valence band, thus creating mobile holes. It has been shown that the Fermi levels for the various metals are aligned close to the conduction band within the depletion region. Under these conditions thermal processes are not large enough to create mobile holes. Therefore other processes for hole injection by a metal-depletion layer contact must be considered; a high field process is the most likely possibility. The emission of carriers over a high potential barrier by a field degradation of the potential barrier is commonly called the Schottky effect. The Schottky effect has been shown to be the injection mechanism in certain types of thin film devices.(ls) SIMPSON and ARMSTRONG recently identified, as Schottky emission, the current mechanism in reverse-biased point injection contact diodes. The Schottky effect will now be employed to explain the injection of holes by a metal-depletion layer contact.
234
P. G.
SEDLEWICZ,
R.
E.
ONLEY
POLLACK(13’ has employed the following form of the Schottky equation to describe the characteristics of a metal-insulator contact:
I =
AST2
-
exp-
44ms kT
exp
C( V/Kay2 T
(7)
where S is the effective area of the contact, A is the Richardson equation constant, a is the effective length through which the field acts, and drns is the energy difference between the Fermi level of the metal and the top of the valence band. The constant C equals
The effective area, S, is difficult to determine because of the inherent irregularities of a metal pressure contact. Also, the effective length, a, can only be considered an approximate value. Equation (7) assumes that the potential distribution is a linear relationship w-ith distance below the probe. This is not the case, since there is a complicated interaction between the field distribution of the depletion region and the biased probe. It has been determined experimentally that the distance, a, is less than the width of the depletion region below the probe. In the present investigation this was demonstrated by testing injection at different points above the junction within the depletion region and observing that no change occurred in the magnitude of the injection current. When Equation (7) is plotted as log 1 vs. I’112 the height of the potential barrier can be obtained from the intercept at v = 0 and is given by #ms = y(ln
ASTZ-
InI).
and C. R. KANNEWURF
voltage and then saturates, which is due to thermally generated holes. With a further increase in the injection voltage the field increases to the point where the barrier for holes is degraded, as indicated by the linear region of the injection curve. This type of curve was observed for all metal probes investigated for hole injection. Table 2 gives a list of the potential differences between the Fermi levels of the metals and the top of the valence band, denoted by (bms. Using Equation (8), 4,s was calculated with the values obtained from the various experimental curves. The potential energy difference for all probes is in the neighborhood of 0.6 eV, indicating that the Fermi level of the various probes is closer to the conduction band than to the valence band. The value of the distance through which the field acts is calculated using Equation (9) and the values are given in Table 3. Using these values of a an approximate value for the initial field is calculated to be greater than 105 V per cm, which is well within the range of values expected for the Schottky effect. Table 2. Energy difference between the Fermi level of the metal a?ld the valence band ___________. ______. Probe
'&mAverage(~V)
Tungsten
0.58 -
Zinc Gold Aluminum Cadmium
(8)
0.61 0.64 0.59 0.60
--
The slope of the linear region of the curve can be used to obtain an approximate value for a even though a linear relationship does not strictly exist between the field and the potential. After differentiating Equation (7), we have
Probe
ax 10-5(m) --
cs
a=------k( TM)2
Table 3. Effective lengths through which the field acts ___.___
(9)
where M is the slope of a plot of log I vs. L’li2. Figures 4 and 5 show hole injection for the various metal probes as a Schottky plot. The current initially increases very rapidly with the
Tungsten
1.42
Zinc
1.5 1.2 2.1 2.9
Gold Aluminum Cadmium
ELECTRON
AND
HOLE
INJECTION
0
w
A
AI
v
Au
BY A METAL-DEPLETION
+x ,03(OK-‘) FIG. 11. Hole injection as a function plotted as log I/T2 vs. l/T.
of temperature
The temperature dependence of hole injection is shown in Figs 9 and 10 for the W and Al probes respectively. The temperature dependence, replotted as log I/T2 vs. l/T, is shown in Fig. 11. (Hole injection data for the gold probe have also been included in this figure.) The three probes show a linear dependence except at low temperatures. This variation has been explained by POLLACK@) in terms of other mechanisms predominating at low temperatures. 7. CONCLUSIONS
The injection of electrons and holes by various metal pressure contacts in the depletion region of beveled p-n wafers has been experimentally studied. The inherent difficulties with a pressure contact created many problems in obtaining reliable data on electron and hole injection. The electron injection characteristics for the various probes were shown to be different from the hole injection characteristics. Electron injection ex-
LAYER
CONTACT
235
hibited a linear relationship when plotted on a log I vs. log V format, whereas hole injection followed a linear relationship when plotted as log I vs. V/2. These graphical representations showed electron injection to be of the space-charge-limited type and hole injection to be of the Schottky emission type. The temperature dependence of electron injection substantiated the space-charge-limited current mechanism whereas the temperature dependence of hole injection gave further evidence of the Schottky-type emission. In addition, for the case of hole injection, it was possible to calculate values for the energy difference between the metal Fermi level and the valence band, and an approximate value for the distance through which the field acts. The proposed energy band model for the metal-depletion layer contact appears to be in agreement with both the space-charge-limited current for electron injection and the Schottkytype current for hole injection.
Acknowledgements-We are grateful to Dr. G. WERTWIJN of the Fansteel Metallurgical Corporation (formerly of Hoffman Electronics) for his initial encouragement and donation of the silicon wafers. We would like to thank Mr. J. C. MCANULTY, Director of the Aerial Measurements Laboratory, for his support and cooperation during this investigation. REFERENCES 1. G. L. PEARSON, W. T. READ and W. SHOCKLEY, Phys. Rev. 85, 1055 (1952). 2. W. G. MATTHEI and F. A. BRAND, J. Appl. Phys., 28, 513 (1957). 3. W. GKRTNER, Proc. Inst. Radio Engrs. 45, 1392 (1957). 4. H. STATZ, R. A. PUCEL, and C. LANZA, Pvoc. Inst. Radio Engrs 4.5, 1475 (1957). 5. J. M. LAVINE, W. RINDER, B. NOST and R. NELSON Trans. Inst. Radio Engrs. ED-8, 252 (1961). 6. J. M. LAVINE, Solid-State Electron. 5,39 (1962). 7. J. M. LAVINE, Solid State Electron. 1, 107 (1960). 8. C. T. SAH, R. N. NOYCE and W. SHOCKLEP,Proc. Inst. Radio Engrs 45, 1228 (1957). 9. N. F. MOTT and R. W. GURNEY, Electronic Processes in Ionic Crystals, p. 168. Oxford Press, London (1936). 10. R. W. SMITH and A. ROSE, Phys. Rev. 97, 1531 (1955). 11. G. T. WRIGHT, Proc. Inst. Elec. Engrs 106, 915 (1959). 12. A. ROSE, Phys. Rev. 97, 1538 (1955). 13. S. R. POLLACK,J. Appl. Phys. 34,877 (1963). 14. J. H. SIMPSON and H. L. ARMSTRONG, J. Appl. Phys. 24, 25 (1953).
Electronics
Pergamon
Press 1964. Vol. 7, pp. 225-235.
Printed in Great Britain
ELECTRON AND HOLE INJECTION BY A METALDEPLETION LAYER CONTACT* P. G. SEDLEWICZt, Electrical
Engineering (Received
R. E. ONLEYI
Department 20 August
and
Northwestern
1963
; in rewisedform
C. R. KANNEWURF University,
Evanston,
14 October
Illinois
1963)
Abstract-The injection of electrons and holes by various metal probes into the depletion region of a beveled silicon p-n diode was experimentally studied. The electrical and thermal properties of metal pressure contacts are presented and used to identify the nature of the injection mechanism. The characteristics of electron injection are shown to be of the space-charge-limited type and the hole injection characteristics follow a high field process. A potential energy diagram of the metaldepletion layer contact is presented and appears to be in agreement with the observed injection phenomena. RBsumC-L’injection d’6lectrons et trous par diverses sondes mt%alliques dans la rCgion d’kpuisement d’une diode au silicium biseautee a CtC BtudiCe expkrimentalement. Les propri&Cs Clectriques et thermiques des contacts & pression de m&al sent prCsentCes et employees g identifier la nature du mkcanisme d’injection. Les CaractCristiques de l’injection d’klectrons sent dCmontrCes comme &ant du type & charge d’espace limit&e et les CaractCristiques d’injection des trous suivent un pro&d& de champ blev& Un schema d’Cnergie potentielle du contact de la couche d’epuisement est pr&entC et semble &tre en accord avec la phCnom&e d’injection obserd. Zusammenfassung-Die Injektion von Elektronen und LBchern mit Hilfe verschiedener Metallsonden in die Sperrschicht einer abgeschrlgten Silizium-p-n-Diode wurde experimentell untersucht. Die elektrischen und thermischen Eigenschaften metallischer Druckkontakte werden dargestellt und dienen zur AufklLrung des Injektonsmechanismus. Die Kennlinien fiir Elektroneninjektion zeigen einen durch Raumladung begrenzten Strom, die fiir die Lccherinjektion eine Emission nach Schottky. Ein Diagramm der potentiellen Energie des Kontaktes zwischen Metal1 und Sperrschicht wird angegeben; es scheint mit den beobachteten Injektionserscheinungen iibereinzustimmen.
1. INTRODUCTION
presented the “spacistor”, a high frequency transistor also using contacts in the depletion the depletion region of a reverse biased p-n wafer region. These groups investigated the two-port parameters of the device and discussed injection was first reported by PEARSON, READ and SHOCKLEY.(~) Following this work MATTHEI and only from a qualitative point of view. LAVINE, BRAND,(~) and GiiRTNERt3) developed high freRINDER, NOST and NELSON,(~) continued the work quency transistors using an injection contact in the with the “spacistor”. LAVINE(~~~) developed a depletion region. STATZ, PUCEL and LANZA@) device with n- and p-doped contacts within the depletion region and made an analysis, which * This work was supported in part by the U.S. Navy predicted the current to be space-charge-limited. Bureau of Weapons, Contract NOW 62-0749-d. This paper is a portion of a thesis submitted by P. G. SedleThe experimental investigation presented here wicz in partial fulfilment of the requirements for the describes the electron and hole injection characterdegree of Master of Science at Northwestern University. istics of various metal pressure contacts within the 7 Present address: hp Associates, Palo Alto, Calidepletion region of beveled p-n silicon wafers. fornia. In addition to the electrical properties of injection, $ Aerial Measurements Laboratory, Northwestern some thermal properties are also discussed. University. THE injection
3
of carriers
from
a metal
contact
into
225
226
P.
2. PREPARATION
G.
SEDLEWICZ,
OF SAMPLES
AND
R. E. ONLEY
and
C.
R.
KANNEWURF
PROBES
In order to investigate the injection of carriers into the depletion region, a wide depletion region at the surface of the sample is desirable. Standard p-n silicon discs were formed by a deep diffusion of acceptors from a constant surface type concentration.* The p-n discs were 10 mils thick, 0.75 in. dia. and had gold plated electrodes on both sides. The n-type substrate was high resistivity material, 100 Q-cm or greater. In order to obtain a wide depletion region at the surface, the p-n discs were beveled across the junction at angles between 1 and 2”, polished, and then etched in a standard CP-4 solution. The metals tungsten, aluminum, gold, zinc and cadmium were selected for the probe materials because they could be worked to a fine point and could withstand the force necessary to achieve a good pressure contact. Also, these metals have reasonably different work functions. Most of the tests were made with the tungsten probe because of its somewhat more durable point. 3. EXPERIMENTAL ARRANGEMENT The electrical connection to the p-side of the beveled p-n wafer was made by soft soldering the wafer to a brass disc which was mounted on the bed of a Wilder probing stage. A pressure contact was used to make the electrical connection to the gold plated n-side of the p-n wafer. A pivot arm was positioned over the bed of the stage so that the various metal probes could be accurately positioned in the depletion region. Figure 1 is a pictorial diagram of the experimental arrangement. Relative dimensions of the depletion region and angle of the bevel have been exaggerated in the diagram for clarity. With an angle of 2” the movement of the depletion region on the surface will be geometrically increased approximately 30 times that of the bulk movement. The curvature of the depletion region at the surface was discussed by LAVINE(~)and it has been experimentally determined to be very slight. This indicates that the major increase at the surface of the depletion region is determined geometrically. Since the resistivity of the n-side of the junction is several orders of magnitude greater than that of the p-side, the movement of the depletion region * The p-n discs were donated by Hoffman Electronics Company, Evanston, Illinois.
FIG.
1. Metal-depletion
layer
injection
arrangement.
can be considered to be entirely into the n-material. One electrical circuit was employed to reverse bias the beveled p-n wafer and another to apply various potentials to the metal probe. The microammeters, In and I,, read the leakage current through the p-n diode when the probe circuit is open. With the probe connected to a high impedance voltmeter, the potential distribution on the beveled surface can be determined and the probe can be located within the depletion region at any floating potential, V~O.The floating potential is defined as the potential of any point within the depletion region relative to the p-side of the wafer. When the probe is biased positively with respect to the floating potential, holes are injected; the high field within the depletion region sweeps the holes to the p-side of the wafer; and the injection current, indicated by microammeter If, adds to the leakage current 1,, while In remains constant. When the probe is biased negatively with respect to the floating potential, electrons are injected; the field sweeps the electrons to the n-side of the wafer; and the current lr adds to the leakage current In, while 1, remains constant. Distortion of the depletion region by a metal pressure contact, which causes irregularities in the injection current, was minimized by using contacts with a diameter of two mils or less. The pressure applied to the metal point contact was varied from 6 x 10s to 3 x 1010 dynes per ems. There were no changes in the injection characteristics due to this pressure variation only.
ELECTRON
AND
4. ELECTRON
HOLE
AND
HOLE
INJECTION
BY A METAL-DEPLETION
INJECTION
I
CONTACT
227
probe potential for all values of voltage greater than the floating potential at the probe point. The same general characteristics were obtained from a number of samples of which two typical curves are shown in Figure 4. Variations in the magnitude of
Figure 2 shows electron injection with tungsten probes, where the voltage, V,, is the probe potential for all values of voltage less than the floating potential at the contact point. The two
102_
LAYER
I
l
I
IL
.8 TUNGSTEN
PROBE .-
;
.=;e,
;
.*
0
:
3. .
.
I-
.
. ,/
: to” .
E
.
-
. /
.
’
l
(Cl
.
s . f5 F 0
. 2.
.r”
IO’
5
t
_,,
.
l
.
IO
W z’
z 0 E lo-2b 0 W -J W
.
.
.
.*
.
.
:
.f
,. /
.*
1O-3
IO0
IO’ V” (volts)
FIG. 2. Electron injection for the tungsten probe (V,
curves shown are typical for all samples and for various probe positions. In most cases samples were reverse biased at 115 V and the probe was positioned at a floating potential of approximately 55 V. The curves are seen to have the same slope but are separated by an order of magnitude, which is generally the range covered with the samples investigated. Typical electron injection curves for the Al, Au, and Zn probes are shown in Fig. 3. Figure 4 shows a plot of hole injection for a 1 mil tungsten probe where the voltage, VP, is the
IO2 < Vfo).
the injection current and in the slope of the linear region were observed. The hole injection curves showed a very rapid initial increase, then a transition region, followed by a constant slope over several orders of magnitude. The magnitude of the hole injection current was always less than that of the electron injection current where 1VP1 = 1J&l. Hole injection for the Au, Al, Zn, and Cd probes is shown in Fig. 5. A comparison of the various graphical representations for hole and electron injection data will be given in Section 6.
P. G. SEDLEWICZ,
228
R. E. ONLEY
and C. R. KANNEWURF
i’ .. .
l. l.
(SduD T’) lN3kl~Il3
0
0
N01133rNI
a
b D
a
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D a
0
D a
O
II
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-2
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II
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In
T 0-
OO
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h
N ‘0
NOU13313
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moo ‘0
%
ELECTRON
in
AND HOLE INJECTION
BY A METAL-DEPLETION
LAYER CONTACT
229
injection curves. Hole injection for the tungsten probe was stable except at low temperatures where breakdown was observed. This may be attributed to the presence of moisture on the surface of the sample. This series of curves shows an increase in injection current and a decrease in the slope, with increasing temperature. Although not presented here, similar results to that of Al and W were also obtained for both electron and hole injection as a function of temperature with gold probes in the depletion region.
‘o’r----J
E IO0
0 i
6. DISCUSSION a. Contact model The experimental data presented in Sections 4 and 5 show the electron injection characteristics of a metal-depletion layer contact to be different from those of hole injection. Electron injection exhibits a linear relationship when plotted as log Ivs. log V, whereas hole injection exhibits a linear relationship when plotted as log I vs. VI/s; o Zn probe also the temperature dependence of electron A Al probe injection is different from that of hole injection. + Cd probe LAVINEt7) has discussed the characteristics of nv Au probe and p-doped contacts in a depletion region and has described potential energy diagrams for these contacts. A potential energy diagram of a metalg lo ’ ’ depletion layer contact and its relation to hole and I B electron injection will now be discussed. (volts) In the depletion region mobile electrons and FIG. 5. Hole injection for the Zn, Al, Cd, and Au probes holes have been removed by the high field leaving (VP > vfo). a space charge of donor and acceptor ions. SAH, NOYCE and SHOCKLEY@)have investigated the 5. INJECTION AS A FUNCTION OF location of the quasi-Fermi levels within the TEMPERATURE depletion region. They describe the potential Injection as a function of temperature was in- diagram within the depletion region and show the potential gradient, valence and conduction vestigated for the W, Al, and Au probes. Measurements were made in a temperature range from bands, a quasi-Fermi level for electrons, & and a level for holes, &. The relationship -50 to +lOO”C. Figures 6 and 7 show the quasi-Fermi between the carrier concentrations and the electron injection curves for the W and Al probes levels can be exwith temperature as a parameter. Electron in- positions of the quasi-Fermi pressed as follows: jection for the tungsten probe showed very little variation with temperature except below room n = nc expp(‘n-flr) (1) temperature. The final slope of the injection kT current did not change over the temperature range investigated. (2) Figures 8 and 9 show hole injection for the W and Al probes respectively with temperature as a where (& - #) represents the separation in potential parameter. The hole injection data were taken under the same conditions as those for the electron between & and the mid-gap position. Equations
VPF
230
P. G. SEDLEWICZ,
R. E.
-0
I
I
(SduJo
i
OO
(SduD”)
II
ONLEY
II
‘+I
‘0
N01133rNI
I
Ii
lN3tltln3
C. R. KANNEWURF
N 0-
lN3UkJfl3
I
and
I
N01133l’NI
3lOH
I
II
NO813313
I
I
“0-
ELECTRON
AND HOLE
INJECTION
BY A METAL-DEPLETION
LAYER
5 i 5 &J 2 Z $ F 2 $ W
p
231
as 4kT/q units below mid-gap and to extend to 12kT/q units below mid-gap and I+$, to have a similar range above mid-gap. In the depletion region the valence band will TUNGSTEN PROBE be partially empty, a fixed number of ionized donors and acceptors will be present, and a space 10’ charge of electrons will be established. Figure 10 shows the proposed metal-depletion layer contact. In the vicinity of the probe all effects due to surface states and oxide contamination layers have been neglected. It is assumed that the extent of too the depletion region is small enough that the potential gradient need not be shown. The location of the Fermi level, &, for the various metal probes relative to the valence and conduction bands (as shown in Figure 10) will id’ now be considered. Measurements of the forward and reverse V-I characteristics for the various probes positioned in the n-type region indicated the contacts to be ohmic in all cases. Therefore the Fermi level for these various metals must lie between mid-gap and the conduction band. Since lo-2 this is a high resistivity n-type material, the Fermi level of the neutral material must be several kT/q units above mid-gap. The position of the Fermi level of the metal has now been located relative to the quasi-Fermi levels within 10-3 8 9 IO I I the depletion region. Before contact is made 0 I 2 34567 I I between the metal and the depletion region, the (“01 t Fermi level of the metal is very close to the quasiP Fermi level for holes. When contact is made FIG. 8. Hole injection for the tungsten probe with temperature as a parameter. the Fermi energy levels in equilibrium must be at the same energy level, which requires the Fermi level of the metal to align itself with the quasi(1) and (2) can be used to define the shift of the quasi-Fermi levels from the mid-gap positions as Fermi levels, C& and &,. The location of the quasiFermi level, &,, can be considered, for simplicity, follows : to be approximately the same as &. This locates kT n A+, = -ln& between SkT/q units and 24kTlq units below (3) ni Q &. The level, &, can align itself with & and & if a space charge of electrons exists in the conA+, = krln?. duction band at the interface. Electrons from the 4 P metal can establish this space charge and the The location of A& and A&, on a potential energy magnitude can be approximated, as discussed by diagram will be determined by n and p. Since the MOTT and &mm-,(~) by the following equation : concentration of electrons and holes in the space charge region is much less than nt, the intrinsic exp - q($m - 44 (5) concentration, & will be located below the midkT gap and & will be located above mid-gap. SAH et al.(s) have estimated the range for A+, and where q(&--&) is the energy difference between A&. These estimates have shown cjn to be as close the Fermi level of the metal and the quasi-Fermi IO2
‘;; a.
CONTACT
VT
2
312
232
P. G. SEDLEWICZ,
R.
E.
ONLEY
and
C.
R.
KANNEWURF
FIG. 9. Hole injection for the aluminum probe with temperature as a parameter.
level for electrons. In view of the preceding discussion this can be considered equal to 2A4,. Using the value of A$, given by SAH et al.,@) No can vary from 3 x 1011 to 3 x 101s electrons per cm3 at the interface. b. Electron Injection The characteristics of the depletion region are to some degree more like those of an insulator than of a semiconductor. There are a negligible number of mobile carriers and a fixed space charge is established. MOTT and GURNEY(~)showed that an insulator without mobile carriers can maintain a current if electrons are raised into an energy band that is normally empty. Electrons can be thermally excited from the metal contact to the conduction band of the insulator if the energy gap is much less
than 1 eV. For this situation the dependence of the current on the voltage is said to be spacecharge-limited and Mott and Gurney give the following equation for the current density:
where L is the thickness of the sample. Recently, several authors have extended Mott and Gurney’s work to include the effects of traps, surface barriers, and lattice defects.(lsJr) ROSE has shown that the V-I characteristics in cadmium sulfide initially follow an Ohm’s law relationship and then make a transition to a region of spacecharge-limited current. It will now be shown that the experimental data for electron injection follow a space-charge-limited relationship.
ELECTRON f $
Electron
AND
HOLE
INJECTION
BY A METAL-DEPLETION
+Metal
I
Depletion
Region
-w
energy diagram of the metal-depletion layer contact.
Electron injection is shown in Figs 2 and 3 on a log-log plot. As the injection voltage increases, the curve makes a transition to a linear region with a slope of approximately 2. This type of behavior can be identified with a space-charge-limited current. Some variation in the slope of the linear region from the ideal slope of 2-O was found to occur; ROSE observed a similar type of variation in cadmium sulfide which was attributed to nonohmic contacts. The onset of the region also varied from probe to probe and from sample to sample. This can be related to changes in the barrier height at the interface. The final slope for the various metal probes is tabulated in Table 1. Table
CONTACT
233
however, that for the various probes the initial slope was approximately unity, which is characteristic of space-charge-limited current at low voltages. The total space charge should not vary with temperature but the fraction of the charge which is free for conduction should increase exponentially.(la) Therefore the electron injection curves should translate with temperature. This was investigated for electron injection and is shown in Figs 6 and 7. The slope of the injection curves for all the various probes was maintained throughout the temperature range tested.
Potential
FIG. 10. Potential
LAYER
1. Slope of electron injection curves
Probe
Slope (average values)
Tungsten
2.0
45
Zinc Gold Aluminum
1.9 1.7 1.9
12 10 9
Number
-
of trials
The initial slope of electron injection was not tabulated because of the greater experimental errors at the low voltages. It was observed,
c. Hole injection The mechanism for electron injection cannot be applied to hole injection for the metal-depletion layer contact. Electron injection, which has been identified as a space-charge-limited process, requires an ohmic contact, the existence of a space charge region, and a small energy gap between the Fermi level of the metal and the conduction band. Hole injection exhibits none of these characteristics. The model presented for the metal-depletion layer contact shows a partially filled valence band, a large energy gap between the valence band and the Fermi level of the metal, and no space-charge region of holes. The injection of holes by a metal-depletion layer contact can be accomplished by removing electrons from the valence band, thus creating mobile holes. It has been shown that the Fermi levels for the various metals are aligned close to the conduction band within the depletion region. Under these conditions thermal processes are not large enough to create mobile holes. Therefore other processes for hole injection by a metal-depletion layer contact must be considered; a high field process is the most likely possibility. The emission of carriers over a high potential barrier by a field degradation of the potential barrier is commonly called the Schottky effect. The Schottky effect has been shown to be the injection mechanism in certain types of thin film devices.(ls) SIMPSON and ARMSTRONG recently identified, as Schottky emission, the current mechanism in reverse-biased point injection contact diodes. The Schottky effect will now be employed to explain the injection of holes by a metal-depletion layer contact.
234
P. G.
SEDLEWICZ,
R.
E.
ONLEY
POLLACK(13’ has employed the following form of the Schottky equation to describe the characteristics of a metal-insulator contact:
I =
AST2
-
exp-
44ms kT
exp
C( V/Kay2 T
(7)
where S is the effective area of the contact, A is the Richardson equation constant, a is the effective length through which the field acts, and drns is the energy difference between the Fermi level of the metal and the top of the valence band. The constant C equals
The effective area, S, is difficult to determine because of the inherent irregularities of a metal pressure contact. Also, the effective length, a, can only be considered an approximate value. Equation (7) assumes that the potential distribution is a linear relationship w-ith distance below the probe. This is not the case, since there is a complicated interaction between the field distribution of the depletion region and the biased probe. It has been determined experimentally that the distance, a, is less than the width of the depletion region below the probe. In the present investigation this was demonstrated by testing injection at different points above the junction within the depletion region and observing that no change occurred in the magnitude of the injection current. When Equation (7) is plotted as log 1 vs. I’112 the height of the potential barrier can be obtained from the intercept at v = 0 and is given by #ms = y(ln
ASTZ-
InI).
and C. R. KANNEWURF
voltage and then saturates, which is due to thermally generated holes. With a further increase in the injection voltage the field increases to the point where the barrier for holes is degraded, as indicated by the linear region of the injection curve. This type of curve was observed for all metal probes investigated for hole injection. Table 2 gives a list of the potential differences between the Fermi levels of the metals and the top of the valence band, denoted by (bms. Using Equation (8), 4,s was calculated with the values obtained from the various experimental curves. The potential energy difference for all probes is in the neighborhood of 0.6 eV, indicating that the Fermi level of the various probes is closer to the conduction band than to the valence band. The value of the distance through which the field acts is calculated using Equation (9) and the values are given in Table 3. Using these values of a an approximate value for the initial field is calculated to be greater than 105 V per cm, which is well within the range of values expected for the Schottky effect. Table 2. Energy difference between the Fermi level of the metal a?ld the valence band ___________. ______. Probe
'&mAverage(~V)
Tungsten
0.58 -
Zinc Gold Aluminum Cadmium
(8)
0.61 0.64 0.59 0.60
--
The slope of the linear region of the curve can be used to obtain an approximate value for a even though a linear relationship does not strictly exist between the field and the potential. After differentiating Equation (7), we have
Probe
ax 10-5(m) --
cs
a=------k( TM)2
Table 3. Effective lengths through which the field acts ___.___
(9)
where M is the slope of a plot of log I vs. L’li2. Figures 4 and 5 show hole injection for the various metal probes as a Schottky plot. The current initially increases very rapidly with the
Tungsten
1.42
Zinc
1.5 1.2 2.1 2.9
Gold Aluminum Cadmium
ELECTRON
AND
HOLE
INJECTION
0
w
A
AI
v
Au
BY A METAL-DEPLETION
+x ,03(OK-‘) FIG. 11. Hole injection as a function plotted as log I/T2 vs. l/T.
of temperature
The temperature dependence of hole injection is shown in Figs 9 and 10 for the W and Al probes respectively. The temperature dependence, replotted as log I/T2 vs. l/T, is shown in Fig. 11. (Hole injection data for the gold probe have also been included in this figure.) The three probes show a linear dependence except at low temperatures. This variation has been explained by POLLACK@) in terms of other mechanisms predominating at low temperatures. 7. CONCLUSIONS
The injection of electrons and holes by various metal pressure contacts in the depletion region of beveled p-n wafers has been experimentally studied. The inherent difficulties with a pressure contact created many problems in obtaining reliable data on electron and hole injection. The electron injection characteristics for the various probes were shown to be different from the hole injection characteristics. Electron injection ex-
LAYER
CONTACT
235
hibited a linear relationship when plotted on a log I vs. log V format, whereas hole injection followed a linear relationship when plotted as log I vs. V/2. These graphical representations showed electron injection to be of the space-charge-limited type and hole injection to be of the Schottky emission type. The temperature dependence of electron injection substantiated the space-charge-limited current mechanism whereas the temperature dependence of hole injection gave further evidence of the Schottky-type emission. In addition, for the case of hole injection, it was possible to calculate values for the energy difference between the metal Fermi level and the valence band, and an approximate value for the distance through which the field acts. The proposed energy band model for the metal-depletion layer contact appears to be in agreement with both the space-charge-limited current for electron injection and the Schottkytype current for hole injection.
Acknowledgements-We are grateful to Dr. G. WERTWIJN of the Fansteel Metallurgical Corporation (formerly of Hoffman Electronics) for his initial encouragement and donation of the silicon wafers. We would like to thank Mr. J. C. MCANULTY, Director of the Aerial Measurements Laboratory, for his support and cooperation during this investigation. REFERENCES 1. G. L. PEARSON, W. T. READ and W. SHOCKLEY, Phys. Rev. 85, 1055 (1952). 2. W. G. MATTHEI and F. A. BRAND, J. Appl. Phys., 28, 513 (1957). 3. W. GKRTNER, Proc. Inst. Radio Engrs. 45, 1392 (1957). 4. H. STATZ, R. A. PUCEL, and C. LANZA, Pvoc. Inst. Radio Engrs 4.5, 1475 (1957). 5. J. M. LAVINE, W. RINDER, B. NOST and R. NELSON Trans. Inst. Radio Engrs. ED-8, 252 (1961). 6. J. M. LAVINE, Solid-State Electron. 5,39 (1962). 7. J. M. LAVINE, Solid State Electron. 1, 107 (1960). 8. C. T. SAH, R. N. NOYCE and W. SHOCKLEP,Proc. Inst. Radio Engrs 45, 1228 (1957). 9. N. F. MOTT and R. W. GURNEY, Electronic Processes in Ionic Crystals, p. 168. Oxford Press, London (1936). 10. R. W. SMITH and A. ROSE, Phys. Rev. 97, 1531 (1955). 11. G. T. WRIGHT, Proc. Inst. Elec. Engrs 106, 915 (1959). 12. A. ROSE, Phys. Rev. 97, 1538 (1955). 13. S. R. POLLACK,J. Appl. Phys. 34,877 (1963). 14. J. H. SIMPSON and H. L. ARMSTRONG, J. Appl. Phys. 24, 25 (1953).