2216 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 53, NO. 9, SEPTEMBER 2006

I–V Characterization of Tunnel Diodes andMultijunction Solar Cells

Wolfgang Guter and Andreas W. Bett

Abstract—This paper discusses common difficulties in measur-ing tunnel diodes and sets a special focus on devices consisting oftunnel diodes and solar cells, such as multijunction solar cells. Theresulting theoretical current–voltage (I–V ) characteristics of tun-nel diodes and solar cells when measured via four-wire techniquesare calculated and compared with experimentally measured I–Vcurves. Solutions to overcome the measurement difficulties areprovided, and a method to infer the maximum tunneling currentdensity of tunnel diodes in a device with solar cells is discussed.This paper also describes how the elsewhere-observed ostensiblehysteresis with multijunction solar cells is caused by the measure-ment setup or by large internal series resistances.

Index Terms—Current–voltage (I–V ) characteristic, multi-junction solar cell, tunnel diode.

I. INTRODUCTION

MONOLITHICALLY stacked multijunction solar cellsbased on III–V semiconductor materials, such as the

GaInP/GaInAs/Ge triple-junction cell, mark the state-of-the-art approach for high-efficiency photovoltaic energy conver-sion [1]–[4]. Because of stacked p-n junctions with differentbandgap energies, these cells can exploit the solar spectrumvery profitably and, hence, reach high efficiencies, such asη ≈ 30% (AM0) and η ≈ 39% (AM1.5d low AOD, C = 236)for application in space or on earth, respectively [5].

The individual subcells of a multijunction cell are inter-connected via Esaki interband tunnel diodes [6]. They featureboth low electrical resistivity and high optical transmissivity.These are the key issues for connecting the cells monolithically[7]–[9].

In this paper, we report on the difficulty to fully characterizemetal–organic vapor phase epitaxy (MOVPE) grown tunneldiodes especially when connected to solar cells.

II. EXPERIMENTAL

A. Structures

An AIXTRON multiwafer MOVPE reactor (AIX2600 G3)with 8 × 4 in configuration was used to grow the test structures.AsH3, PH3, TMGa, TMIn, and TMAl were used as precursors.

Manuscript received January 25, 2006; revised April 20, 2006. This workwas supported in part by the European Commission through the funding ofthe project FULLSPECTRUM (SES6-CT-2003-502620) and by the FederalMinistry for the Environment, Nature Conservation and Nuclear Safety (BMU)under Contract 03285554 F. The work of W. Guter is supported by the DeutscheBundesstiftung Umwelt. The review of this paper was arranged by EditorP. Panayotatos.

The authors are with the Fraunhofer-Institute for Solar Energy Systems,79110 Freiburg, Germany (e-mail: wolfgang.guter@ise.fraunhofer.de).

Digital Object Identifier 10.1109/TED.2006.881051

Fig. 1. Left: Test structure with a tunnel diode grown underneath the associ-ated solar cell (here: GaInAs, middle cell). Right: Test structure with isolatedhigh-bandgap tunnel diode.

SiH4, DETe, DMZn, and CBr4 were employed as dopingsources. Since triple-junction cells are grown on diffusion-activated germanium wafers, all test structures were grown onGe substrates with 6 off-orientation toward [111]. The growthconditions were p = 100 mbar, T = 560−700 C and V/III =1−50 for arsenides and 110–230 for phosphides.

Three different types of structures have been made, which arelisted as follows:

1) tunnel diodes within a triple-cell structure;2) tunnel diodes underneath a single-junction cell (Fig. 1,

left);3) isolated tunnel diodes (Fig. 1, right).

The tunnel diode consists of the tunnel junction itself madeby one degenerately doped n++ and one p++ layer as well astwo enclosing barrier layers with the purpose of minimizingdopant diffusion [10]–[12].

Tunnel diode peak current densities may exceed values of10 A/cm2. In order to measure such high current densities, wedesigned a special layout for the test devices. These have frontcontact dots of various areas (0.283–6.605 mm2) uniformlyspread over the whole wafer as well as a segment for later Hall,ECV, OPL, SIMS, etc. measurements. All test structures aremesa-etched.

In order to minimize contact resistivity, a Cr/Zn/Au/Nip-frontside contact with a resistivity of rc < 1 mΩ · cm2

was applied instead of the standard Ti/Pd/Ag contact

0018-9383/$20.00 © 2006 IEEE

GUTER AND BETT: I–V CHARACTERIZATION OF TUNNEL DIODES AND MULTIJUNCTION SOLAR CELLS 2217

Fig. 2. Simplified voltage sweep setup for the measurement of the I–Vcharacteristic of a test structure (device), i.e., tunnel diode or solar cell.The voltage Uappl can be ramped, the actual voltage drop over the deviceU is measured directly, and the current is derived via Rmeas. RS is anadditional serial resistance that is used to simulate internal resistance in chaptersA and C.

Fig. 3. Left: Equivalent circuit diagram of a test structure with isolated tunneldiode. Right: Simulated influence of RS,int on the I–V characteristic. Thedotted graph represents the characteristic of a tunnel diode. A high internalresistance shifts the graph to the solid line. An instable region in the I–Vcharacteristic with up to three possible current densities for one voltageemerges. During the measurement, the tunnel diode keeps to its mode ofoperation. Hence, sweeping up the voltage causes the 0−A−A′−C transitionand sweeping down the voltage causes the C−B−B′−0 transition.

(rc = 9 mΩ · cm2). The whole backside was covered with aNi/AuGe/Ni n contact (rc = 4 µΩ · cm2). Finally, a 2-µm layerof Au was superimposed on the contacts via electroplating. Thismaximizes transversal conductivity and protects the underlyingcontact against scratching.

B. Measurement Setup

Current–voltage (I–V ) characterization was performed via afour-line measurement technique (Fig. 2). The voltage sourceprovides Uappl and is connected to the device in line witha high-precision measurement resistor Rmeas, which can bevaried from 10 mΩ to 10 kΩ with an error of 0.02%. The voltagedrop U over the device can be measured directly via a digitalmultimeter (error < 0.002%). The current through the devicecan be inferred from the voltage drop over Rmeas. In order toobtain an I–V curve, the voltage Uappl is swept in uniformsteps via a Kepco bipolar voltage source. A 1.5-mm2 copperwiring was used to keep errors due to electrical losses small.

III. DISCUSSION

The following paragraphs discuss the measurement ofdifferent test structures and introduce their equivalent circuitdiagrams.

A. Test Structures With Isolated Tunnel Diodes

A tunnel diode shows an s-shaped voltage characteristic[6] similar to the dotted line in Fig. 3. Low voltages causehigh tunnel currents through the diode. When the maximum

Fig. 4. Left: Equivalent circuit diagram of a test structure with isolatedtunnel diode. An additional resistor RS was used to simulate high internalserial resistances. Right: Influence of internal serial resistance on the I–Vcharacteristic of a GaAs tunnel diode. The graph with RS = 0 Ω showsthe I–V characteristic of the tunnel diode used. Increasing RS (1 Ω) leadsto a sheared I–V curve and then results in a discontinuity (10 Ω). Veryhigh RS (13 Ω) finally causes a different characteristic for the forward andbackward voltage sweeps (hysteresis).

tunneling current density Jpeak is reached, the diode entersa region with negative differential resistance, i.e., tunnelinggets weaker with increasing voltage. Higher voltages causethe current to increase again. This current corresponds to thecommon thermal current of a p-n diode [13].

The isolated tunnel diode test structure can be regarded asa series-connected tunnel diode (TD) and internal resistance(RS,int) caused by the metal, the semiconductor–metal junc-tion, and other semiconductor layers. The left-hand side ofFig. 3 shows an equivalent circuit diagram of such a device. Udenotes the voltage drop over both RS,int and the tunnel diode.

The tunnel diode can only be characterized in combinationwith this internal serial resistance. Fig. 3 shows the calculatedshift in voltage caused by RS,int.

Resistances larger than the negative resistance of the tunneldiode cause an instable I–V characteristic with up to threedifferent operating points for the same voltage. This is due tothe fact that the voltage has several possibilities to distributeover resistance and tunnel diode.

The instable region has two consequences. On the one hand,important features, such as the maximum tunneling current, thepeak-to-valley ratio, as well as the maximum tunneling voltage,will be impossible to acquire with a simple voltage sweep. Onthe other hand, it also causes a different I–V characteristic fora forward and a backward sweep (Figs. 3 and 4). Experimentsconfirmed that the tunnel diode keeps to its operating modeas long as possible. Thus, sweeping up the voltage causes atransition from the maximum tunneling current at A to A′ inFig. 3. Sweeping down the voltage causes a transition from Bto B′. Hence, in order to fully characterize the tunnel diode, alow contact resistance is desirable. This can be achieved withthe experimental methods explained in Section II-A. Variationsof the internal serial resistance RS,int were experimentallysimulated by an additional resistor RS . Fig. 4 shows the shifted

2218 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 53, NO. 9, SEPTEMBER 2006

Fig. 5. Construction of the I–V characteristic of a tunnel diode whenmeasured with the setup in Fig. 2. The solid line shows the characteristic ofthe tunnel diode. The operating points result from the intersections of thiscurve with the dashed lines with slope −1/RS,ext. RS,ext represents theseries resistance caused by Rmeas and the wiring. The applied voltage U1

can cause three different voltage drops over the tunnel diode and, hence,results in three distinct operating points (large dots). Sweeping up the voltagecauses the 0−A−A′−C transition at U2, and sweeping down the voltagecauses the C−B−B′−0 transition at voltage U1. That gives rise not only to adiscontinuity but also to a gap in the I–V curve.

I–V curves with increasing RS and confirms the predictionsin Fig. 3.

B. Measurement of Isolated Tunnel Diodes

When isolated tunnel diode structures are measured with thesetup from Fig. 2, an additional resistance caused by Rmeas

from the setup and by resistance of the measurement wireshas to be regarded. The applied voltage Uappl denotes thevoltage drop over the external serial resistances (RS,ext =Rmeas + Rwires) as well as RS,int and the tunnel diode itself.RS,ext determines the true operating point of the tunnel diodeat external voltages Uappl. Fig. 5 shows the construction of theoperating point.

When RS,ext is smaller than the negative differential resistiv-ity of the tunnel diode, only one intersection and, hence, onlyone operating point can be found (Fig. 5, dotted line throughA). If in addition to that, a small contact resistance has beenprovided, the full I–V characteristic of the tunnel diode can bemeasured.

When RS,ext is larger than the negative differential resistivityof the tunnel diode, some voltages (e.g., U1 and U2 in Fig. 5)can cause more than one operating point of the device again.This fact results in a discontinuity in the ramped voltage dropover the tunnel diode and, consequently, causes a gap in themeasured I–V characteristic. Of course, no discontinuity canbe observed when the current is measured against the externalvoltage Uappl.

The experimentally measured current against voltage drop Uover the device follows different transitions, depending on thedirection of the voltage sweep. Increasing voltage causes thetransition from A to A′ at approximately Jpeak (see Fig. 5).Decreasing voltage causes the transition from B to B′ atapproximately Jvalley (see Fig. 5). These different transitionshave been measured experimentally (Fig. 6).

C. Test Structures With a Tunnel DiodeUnderneath a Solar Cell

For the purpose of simplicity, the solar cell can be regardedas a photodiode with the well-known exponential I–V charac-

Fig. 6. Experimentally measured I–V characteristics of a GaAs tunnel diode(RS = 0; see Fig. 2). A high measurement resistance Rmeas adds to theexternal series resistances RS,ext and causes a wide discontinuity in the curve,which depends on the direction of the voltage sweep. Low Rmeas causes thediscontinuity to almost vanish.

Fig. 7. I–V characteristic of a GaInAs solar cell without illumination (fulldots) and illuminated with the solar spectrum. The illumination generates anegative photocurrent that leads to a curve shifted to lower current densitiescompared to the dark measurement.

teristic. Fig. 7 shows a plot of the measured I–V curves of aGaAs solar cell with and without illumination. Light generatesa negative photocurrent in the cell and shifts the characteristicto lower current values [14].

Test structures consisting of a solar cell with underlyingtunnel diode can be regarded as a series connection of the twodevices (Fig. 8, left). The overall I–V characteristic resultsfrom a superposition of the solar cell characteristic and thetunnel diode characteristic.

Tunnel diode structures with solar cells cannot be charac-terized without light (dark I–V ) because the tunnel diode isconnected in backward direction to the diode of the solar cell.At negative voltages, the solar cell operates in reverse bias andlimits the current flow to almost zero (Fig. 8, right).

With illumination, the solar cell generates a negative pho-tocurrent as explained before (Fig. 7). Conventionally, the I–Vcurve is mirrored into the first quadrant of the coordinate systemfor convenience (Fig. 9, dashed line). The applied voltage

GUTER AND BETT: I–V CHARACTERIZATION OF TUNNEL DIODES AND MULTIJUNCTION SOLAR CELLS 2219

Fig. 8. Left: Equivalent circuit diagram of a test structure with solar celland tunnel diode. Right: Schematic superposition of the I–V characteristics(dark measurement) of the tunnel diode (dotted) and solar cell (dashed). If nophotocurrent is generated, the tunnel diode is in backward operation. The devicecharacteristic (solid) results from the addition of the voltage drops over thesingle devices. The tunnel diode cannot be characterized because of the currentlimitation by the solar cell.

Fig. 9. Schematic superposition of the I–V characteristics from tunnel diode(dotted) and solar cell (dashed), resulting in the solid curve. The current den-sities are plotted in the first quadrant according to the photovoltaic convention.JSC < Jpeak. (a) The tunnel diode works in the operating point with lowestvoltage drop and acts like an almost ohmic resistance. The characteristic of thesolar cell is slightly sheared. Almost no loss in efficiency of the solar cell canbe observed. JSC > Jpeak. (b) For low voltages, the characteristic of the solarcell is strongly sheared to negative voltages, since the tunnel diode operates inthe region dominated by thermal current. At higher voltages, the total devicecurrent rises again and peaks with the maximum tunneling current. The so-produced dip in current density can severely lower the maximum power outputof the solar cell.

distributes over the tunnel diode and the solar cell, but thecurrent through both devices is the same. Two different caseshave to be considered. First, we have

JSC < Jpeak.

If the short-current density of the solar cell JSC is lowerthan the maximum tunneling current Jpeak, for most of thevoltages, the tunnel diode features three different operatingpoints, i.e., three different voltages are possible for almost anycurrent density. However, all experiments confirmed that thetunnel diode was operating in the state with the lowest voltagedrop. Hence, the tunnel diode acts like an almost ohmic resistor

Fig. 10. Measured I–V characteristics of a GaInAs solar cell with GaAstunnel diode. Solid symbols mark a measurement at light concentrations,causing currents lower than Jpeak. Open symbols mark a measurement athigher light concentrations, causing currents that exceed Jpeak at low voltages.The dip in the curve appears at high voltages, when the current from the celldrops below Jpeak.

and hardly reduces the maximum power output of the solar cell(Fig. 9(a)). Second, we have

JSC > Jpeak.

If the short-current density of the cell exceeds the maximumtunneling current, the tunnel diode works in the region wherethermal current dominates and a high voltage drop occurs overthe tunnel diode. The I–V curve of the solar cell is shearedto lower voltages. At high voltages U , the current through thesolar cell falls below Jpeak, and three different operating pointsare available again. The I–V characteristic of the test device(Fig. 9(b)) results from the addition of the voltage drops of thedevices.

When the solar spectrum is concentrated by a factor of 1000on a GaInP/GaInAs/Ge triple-junction solar cell, a short-currentdensity of 14 A/cm2 can be generated (JSC = 14 mA/cm2 at1 × AM1.5d). The maximum tunneling current density has toexceed this value to avoid the dip in the I–V characteristicthat reduces the cell’s efficiency. Fig. 10 shows the I–V char-acteristic of a test structure with solar cell and tunnel diodeat two different illumination concentrations. When the criticalillumination is reached, the cell’s current exceeds the maxi-mum tunneling current of the tunnel diode and a dip appears(see also [15]).

When a large serial resistance exists within the device (e.g.,a large contact resistance), the I–V characteristic is sheared tolower voltages. Analogous to the isolated tunnel diode structure(Section III-A), an instable region in the characteristic canoccur. Consequently, important features, such as the maximumtunneling current or the maximum power point of the solar cell[14] cannot be identified and a different I–V characteristic fora forward and a backward voltage sweep arises (Fig. 11).

Experiments again confirmed that the device keeps to its op-erating mode as long as possible. Thus, sweeping up the voltagecauses a transition from A to A′ in Fig. 11. Sweeping downthe voltage causes a transition from B to B′. Fig. 12 showsthe actual I–V characteristics of a device where the internal

2220 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 53, NO. 9, SEPTEMBER 2006

Fig. 11. Left: Equivalent circuit diagram of a test structure with solar celland underlying tunnel diode. Right: Simulated influence of RS,int on the I–Vcharacteristic. The dotted graph represents the characteristic of a solar cell withhigher JSC than Jpeak. A high internal serial resistance shears the graph tothe solid line. An instable region in the I–V characteristic with up to threepossible current densities for one voltage emerges. During the measurement,the tunnel diode keeps to its mode of operation. Hence, sweeping up thevoltage causes the A − A′ transition, and sweeping down the voltage causes theB − B′ transition.

Fig. 12. Left: Equivalent circuit diagram of a test structure with solar celland underlying tunnel diode. An additional Resistor RS was used to simulatehigh internal serial resistances. Right: Influence of internal serial resistance onthe I–V characteristic of a GaInP/AlGaAs tunnel diode underneath a GaInPsolar cell. The graph with RS = 0 Ω shows the I–V characteristic of thesolar cell used at JSC > Jpeak. Increasing RS leads to a sheared I–V curve(2 and 13 Ω). Very high RS (50 Ω) finally causes a different characteristic forthe forward and backward voltage sweeps (hysteresis).

serial resistance was simulated by an additional resistor. Theshearing of the I–V curve as well as the hysteretic behaviorcan be observed. Thus, a low contact resistance is necessary tofully characterize the solar cell device with the tunnel diode.It can be achieved with the experimental methods explained inSection II-A.

D. Measurement of Tunnel Diodes Underneath a Solar Cell

Fig. 13 shows the construction of the I–V characteristic ofa solar cell with underlying tunnel diode when measured in themeasurement setup in Fig. 2. The serial resistance RS due tothe setup again plays an important role.

If RS is smaller than the negative differential resistivity ofthe tunnel diode, only one intersection of the two characteristicscan be found for any voltage Uappl, and hence, only one

Fig. 13. I–V characteristic of a solar cell with underlying tunnel diode (solid)for JSC > Jpeak. The intersections with the working resistance caused by themeasurement resistance (dashed lines) and with a slope of 1/RS,ext markthe operating points at the applied voltage U . Large serial resistances allowtwo operating points for each voltage U1 and U2. Experimentally measuredI–V curves show the A − A′ transition when the voltage is swept up andthe B − B′ transition when the voltage is swept down. Very small serialresistance (dotted) removes the dependency from the sweeping direction, andJSC < Jpeak completely removes the dip.

operating point exists (Fig. 13, dotted line through B). Thecomplete I–V characteristic of the solar cell with underlyingtunnel diode can be measured.

When RS is larger than the negative differential resistivity ofthe tunnel diode, some voltages (e.g., U1 and U2 in Fig. 13)cause more than one operating point again. This leads inanalogy to the isolated tunnel diode structure to a discontinuityin the ramped voltage drop over the device and, consequently,causes a gap in the measured I–V characteristic. Furthermore,the characteristic depends on the direction of the voltage sweepagain. Sweeping up the voltage (measurement from JSC toVOC) causes a transition from A to A′, leading to a deep dipand a low peak in the characteristic. When the voltage is sweptdown (from VOC to JSC), the transition from B to B′ is caused.This produces a shallow dip and a high peak in the characteris-tic. Fig. 14 shows some forward- and backward-measured I–Vcharacteristics taken with various measurement resistors.

A small measurement resistance removes the dependencyfrom the sweep direction, and JSC < Jpeak removes the dipcompletely.

For many reasons, it is desirable to extract the maximum tun-neling current density from the I–V measurements not only ofisolated tunnel diode structures but also of structures combiningtunnel diodes and solar cells. The thermal load caused by thegrowth of further semiconductor layers above the tunnel diodehas been observed to degrade the tunneling performance [9] forexample. This can be investigated with the structures describedin this section. The height of the observable peaks correspondsto J(A) and J(B′), respectively. However, even J(B) does notnecessarily have the same value as Jpeak; it can be lower. Thisdifficulty can be overcome, and the maximum tunneling currentdensity may be determined. The dip in the I–V characteristicexactly appears, when JSC starts to exceed Jpeak. Varyingthe illumination intensity changes ISC and, hence, allows theprecise measurement of the maximum tunneling current density(compare to Fig. 10).

GUTER AND BETT: I–V CHARACTERIZATION OF TUNNEL DIODES AND MULTIJUNCTION SOLAR CELLS 2221

Fig. 14. Experimentally measured I–V characteristics of a GaInP solarcell with an underlying AlGaAs/GaInP tunnel diode for JSC > Jpeak andRS = 0 (see Fig. 2). The curves are shifted in terms of current to distinguishthem more easily. The real I–V curves lie on top of each other (see inset).A high measurement resistance Rmeas adds to the other external series re-sistances and causes a wide discontinuity in the curve, which depends on thedirection of the voltage sweep. Low Rmeas causes the discontinuity to almostvanish.

E. Measurement of a Multijunction Solar Cell

Multijunction solar cells also consist of a series connectionof solar cells and tunnel diodes. Hence, the measurement of amultijunction cell resembles the measurement of a solar cellwith underlying tunnel diode. It has been observed that theexact shape of the characteristic at high illumination densitiesdepends on the direction of the voltage sweep [16]. This depen-dency from the measurement direction, however, is not neces-sarily caused by the device itself. Similar to the explanationsfrom the previous sections, external serial resistance RS,ext dueto the measurement setup (Fig. 2) is the origin of this effectas long as the internal serial resistance RS,int (due to contactresistances, etc.) is small. The instable region, the discontinuity,and the dependency from the measurement direction can beremoved when these resistances are kept at values smaller thanthe negative differential resistivity of the tunnel diode. Increas-ing the illumination intensity first introduces the expected dipin the forward direction and then in both directions (Fig. 15).

Due to the different transitions explained in Fig. 11, thedip cannot be resolved during the backward sweep for a JSC

that is only slightly higher than Jpeak. However, the forwardsweep proves that it already is present. The maximum tunnelingcurrent density equals the ISC when the first dip in the forwardsweep emerges. The peak of the backward sweep only approx-imately corresponds to Jpeak.

F. Sweeping the Voltage by Use of a Potentiometer

Another measurement setup has been used to characterizestructures consisting of tunnel diodes and solar cells [16]. It issimilar to the four-wire measurement setup in Fig. 2 but sweepsthe voltage by use of an adjustable resistor (Fig. 16, inset). Inthis case, the differences between the I–V curves obtained bya voltage sweep in forward and backward directions are even

Fig. 15. Experimentally measured I–V characteristics of a GaInP/GaInAs/Getriple-junction solar cell, which was taken at increasing intensity of illuminationwith the solar spectrum. When JSC of the cell is smaller than Jpeak of thetunnel diodes, the common solar cell characteristic is measured. At higherilluminations, first, a dip in the forward sweep and then in both sweepingdirections becomes visible.

Fig. 16. Different measurement setup compared to Fig. 2 (inset). A fixedvoltage Ufixed is applied, and the adjustable resistor Rsweep is used to performthe voltage sweep. Arrows mark the resulting transitions.

more blatant (Fig. 16). Since the measurement difficulties dueto series resistances can hardly be avoided with this setup, itis not suitable for the characterization of structures with tunneldiodes.

IV. CONCLUSION

The measurement setup and internal serial resistancewithin structures with tunnel diodes play an important rolein characterization. High internal serial resistances can becaused by lowly doped layers with low conductivity ormetal–semiconductor contacts with high resistivity. High ex-ternal serial resistances can arise from measurement resistorsor unsuitable wiring in the setup. Sweeping the voltage with anadjustable resistor is particularly unsuitable.

To characterize the region with negative differential resis-tance, both the internal and the external serial resistance have

2222 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 53, NO. 9, SEPTEMBER 2006

to be smaller than the negative differential resistance of thetunnel diode. In this case, no difference between forward andbackward measurements will occur.

If the internal serial resistance RS,int is larger than thenegative differential resistance of the tunnel diode, the minimalvalue for RS,int can be inferred. RS,int is larger than the inversegradient of a straight line through points A and B in Fig. 3or 11 for isolated tunnel diodes or a structure with solar cellsand tunnel diodes, respectively. This limit assumes a verticaldrop (infinite negative resistivity) in the I–V characteristic ofthe idealized tunnel diode.

If the external resistance RS,ext is small enough, the full I–Vcharacteristic of structures with solar cells and tunnel diodescan be recorded. In order to avoid any difference betweenforward and backward sweeps, both RS,int and RS,ext have tobe smaller than the negative differential resistance of the tunneldiode.

Since RS,int does not actually have impact on the values forthe peak and valley current densities of an isolated tunnel diodestructure but shears the whole I–V curve in voltage, the valuefor Jpeak can be read off the forward measurement and thevalue for Jvalley can be read off the backward measurement.This does not work properly with structures consisting of solarcells and tunnel diodes. The most precise way to find the valuefor Jpeak is to increase the illumination on the device until adip in the forward characteristic appears. Assuming the shuntresistance of the solar cell is very small, JSC, at this point whenthe dip appears, equals Jpeak.

ACKNOWLEDGMENT

The authors would like to thank Dr. F. Dimroth for manyfruitful discussions and his suggestions. Special thanks go toA. Ohm for processing the solar cell structures and toE. Schäffer for various I–V measurements.

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Wolfgang Guter received the Diploma degree inphysics from the Albert Ludwigs University ofFreiburg, Freiburg, Germany, in 2005, and is cur-rently working toward the Ph.D. degree in physicsat the University of Konstanz, Konstanz, Germany,in cooperation with the Fraunhofer-Institute for SolarEnergy Systems (ISE), Freiburg, which concerns var-ious aspects of high-efficiency III–V multijunctionsolar cells.

From 2000 to 2004, he was setting up an auto-mated measurement facility for heat pump systems

at Fraunhofer-ISE. In 2002, he completed an honors project in physics at theUniversity of New South Wales, Sydney, Australia, supported by a scholarshipfrom Universitas 21. His thesis concerned the fabrication of quantum electrode-vices with bilayer hole systems.

Andreas W. Bett received the Diploma degree inphysics and the Diploma degree in mathematics fromthe Albert Ludwigs University of Freiburg, Freiburg,Germany, in 1988 and 1989, respectively, and thePh.D. degree in physics from the University of Kon-stanz, Konstanz, Germany, in 1992.

He joined the Fraunhofer-Institute for Solar En-ergy Systems, Freiburg, in 1987. Since 1993, hehas been the Head of the “III–V Solar Cells andEpitaxy” Group. His main areas of interest includethe epitaxial growth of III–V semiconductors, char-

acterization techniques, and development of technologies for the fabrication ofdevices, such as solar cells. His current interest is focused on the investigationof concentrator solar cells and concentrator systems, low-bandgap cells forthermophotovoltaics, multijunction solar cells, and demonstration projects.