pn结新模型

Anomalous Differential Resistance Change at the Oscillation Threshold in Quantum-Well Laser Diodes Peter G.Eliseev,Senior Member,IEEE,Pawel Adamiec,Artem Bercha,Filip Dybała,Roland Bohdan,and
Witold A.Trzeciakowski
Abstract—Anomalous behavior is investigated of differential re-
sistance of laser diodes at the lasing threshold.The regular
case is the known decrease of
the associated with a dynamic
saturation of the junction voltage.In contrast to this,the anoma-
lous case is an increase of the differential resistance(the“positive
kink”
of).Some regular samples are found to show the
anomaly at lower temperature or at high hydrostatic pressure.The
anomaly is discussed in terms of the injection-induced conductivity.
Index Terms—Differential resistance,pressure and temperature
effects,semiconductor lasers.
I.I NTRODUCTION
E LECTRICAL diagnostics of laser diode operation in-
cludes determination of the oscillation threshold by kink
of the differential resistance of diode measured as a function
of the pumping current.Corresponding experimental demon-
stration and interpretation had been done in early studies of
homojunction lasers[1],[2]and later in studies of double-het-
erostructure lasers[3]–[5],and of quantum-well lasers[6].
Sometimes,power kinks and spatial mode switching can be de-
tected electrically by observation of variation of the differential
resistance.
The junction voltage in the laser diode contains the contri-
bution of the quasi-Fermi-level
separation that shows a
tendency to saturation above the threshold because of satura-
tion of the modal gain under stationary oscillation.When the
voltage is saturated but current continues to increase,it is equiv-
alent to the disappearance of the differential resistance.This
leads to the regular behavior
of in laser diodes
(is
the total voltage applied to the diode),according to observa-
tions in[1]–[6].Namely this regular behavior is a decrease of
the above the threshold,sometimes down to the residual
Manuscript received June7,2004;revised August11,2004.This work
was supported in part by the NATO Science for Peace Program under Grant
SfP972443.
P.G.Eliseev is with the Center for High Technology Materials,University of
New Mexico,Albuquerque,NM87106USA(e-mail:eliseev@).
P.Adamiec and F.Dybala are with the High Pressure Research Center,Polish
Academy of Sciences,01-142Warsaw,Poland and also with the Institute of
Physics,Warsaw University of Technology,00-662Warsaw,Poland(e-mail:
pa@unipress.waw.pl;fd@unipress.waw.pl).
A.Bercha is with the High Pressure Research Center,Polish Academy of Sci-
ences,01-142Warsaw,Poland and also with the Uzhgorod National University,
88000Uzhgorod,Ukraine(e-mail:artem@unipress.waw.pl).
R.Bohdan is with the High Pressure Research Center,Polish Academy
of Sciences,Sokolowska29/37,01-142Warsaw,Poland(e-mail:roland@
unipress.waw.pl).
W.A.Trzeciakowski is with the High Pressure Research Center,Polish
Academy of Sciences,01-142Warsaw,Poland(e-mail:wt@unipress.waw.pl).
Digital Object Identifier10.1109/JQE.2004.839237
series resistance of the electrodes and bulk
semiconductor.
However,in addition to this regular behavior,there were obser-
vations of anomalous sign of the change
of above the
threshold,particularly in the same device but under different
temperature(see,for example,[5]and[7]where an explana-
tion of this anomaly was also reported).In[8],the analysis of
voltage across the laser diode has been given for the case of elec-
trical response to the external optical feedback.The component
associated with a leakage into claddings is found to have an op-
posite sign to the junction voltage component.In[5]and[7],it
has been shown that the resistance change due to injection-in-
duced conductivity can be responsible for anomaly of threshold
kink of the differential resistance.
In this work we demonstrate the differential electrical charac-
teristics versus
current in several types of laser diodes
in a range of temperature and of pressure.Anomalous cases are
found.Pressure-related anomaly is reported for thefirst time.
We present here also a model explaining qualitatively such pres-
sure-and temperature-related anomalies.
II.E XPERIMENTAL
We studied electrical and optical characteristics of different
types of lasers but here we shall present only three examples
of GaAs–AlGaAs quantum-well(QW)lasers that revealed
anomalous as a function of temperature and pres-
sure.Samples I and II were single-mode SQW diode lasers
with emission wavelengths at850and790nm,respectively.
Both structures were grown by metal–organic chemical vapor
deposition(MOCVD)on an n-type100GaAs:Si substrate.
For an850-nm diode laser the active layer contained one
9-nm-thick QW made of GaAs.The waveguide layers were
made of100-nm-thick
Al
Ga As.The active layer and
the waveguides were nominally undoped.The thicknesses of n
(Si)-and p
(Zn)-Al
Ga As cladding layers were
1.5m.
Both the p-and n-cladding layers were doped to
about
cm.For the790-nm diode,the active layer was made of
9-nm-thick
Al
Ga As QW surrounded by110-nm-thick
waveguides with graded Al concentration varying from45%to
63%.The active region was sandwiched between n(Si)-and
p
(Zn)-Al
Ga As cladding layers with the doping
level
cm.In both samples,a300-nm-thick p-contact
layer was made of GaAs:Zn with doping level higher
than
cm.The threshold currents at ambient conditions
were22mA for Sample I and30mA for sample II.The third
sample was a commercial single-mode laser made by Sanyo
(DL-7140-201)emitting at785nm.The threshold current at
ambient conditions was about30mA.
0018-9197/$20.00©2005IEEE
Fig.1.Plots of IdU=dI versus I at different temperatures for Sample I.The arrows show the values of threshold currents I .
In our pressure/temperature experiments we used a piston-cylinder cell made of maraging steel and operating up to 2GPa.It was described in more detail elsewhere [9].A pure gasoline was used as a pressure medium.The pressure was calibrated with the resistance of InSb sensor that gives about 0.1kbar sen-sitivity in the 20kbar range (the absolute pressure accuracy de-pends on the proper calibration of the sensor and is probably around 1kbar).The light emitted by the laser comes out of the cell through the multimode optical fiber (with 50or 100mi-crometer core)[10].For the temperature control we passed cool nitrogen gas through the copper tube wound around the cell;this method allowed to cool it down to about 120K.The tempera-ture was measured by a thermocouple placed inside the pressure cell and its stability was better than 1K.The cell with cooling elements was placed under a small hydraulic press so that the pressure could be varied at low temperature.In the pressure/tem-perature range where our liquid solidi fies it is necessary to vary the temperature at the fixed position of the piston.In such case the pressure changes when we cool down the cell.Even when the liquid solidi fies the pressure remains hydrostatic (to a good approximation).
For each pressure we measured the
–and the power-cur-rent characteristics together with the spectra at different cur-rents under cw operation.The
derivative was obtained by adding the ac component to the current and detecting the voltage modulation using the lock-in ampli fier.
III.R ESULTS
In Fig.1we show
the as a function of current for Sample I.The kinks at threshold can be clearly seen.At lower temperatures,they change sign.The heights of the kinks (mea-sured vertically between the extrapolated curves
for )are shown in Fig.2.We also show the kink heights for Sample II where a similar anomalous behavior can be observed.In Fig.3the pressure evolution of
the dependencies for Sample III is shown.Above 6kbar the thresholds (denoted by arrows in Fig.3)increased substantially for this laser due to
increased
Fig.2.Heights of the kinks in IdU=dI versus temperature for two lasers (Samples I and II).In both cases the kink changes
sign.
Fig.3.IdU=dI at room temperature (293K)and at different pressures for Sample III.The arrows show the values of threshold currents at each pressure.
leakage to
the minima in the claddings.The anomalous be-havior of the kink height at elevated pressure can be seen in Fig.4,where we display both the kink height (left scale)and the threshold current (right scale).However,for some lasers the effects of pressure were much weaker,as can be seen by the curve for Sample I shown in Fig.4.In this case,the effect of pressure on threshold current was also much weaker.
IV .D ISCUSSION
A.Origins of Anomalous Voltage
There are relatively small corrections to the regular
–curve of diode associated with voltage drop at series structure components sensitive to the laser state of the active region,more speci fically,sensitive to the carrier density in the active layers.One is based on radiation transport inside the diode chip.Another correction is associated with injection-induced conductivity (IIC)provided by drift-diffusion transport in layers adjacent to the junction.
An ideal
–curve of the p-n junction can be represented by
a simple
expression
,
where is junc-tion
voltage,is the so-called saturation current (not related to
ELISEEV et al.:ANOMALOUS DIFFERENTIAL RESISTANCE CHANGE AT THE OSCILLATION THRESHOLD IN QUANTUM-WELL LASER DIODES
11
Fig.4.Heights of the kinks in IdU=dI (left scale,full symbols)and threshold currents (right scale,empty symbols)versus pressure for (a)Sample III and (b)Sample I.
the laser-induced saturation,but related to the saturation under reverse
bias),is the factor that,in the nondegenerate case
is
or (Shockley [11]and Hall [12]cases)
or
in more general case
(is nonideality factor,that increases to
3–4in the case of degeneracy [13])
or
in the case of tun-neling current
(is energy parameter of tunneling mechanism [14]).As the operation
current,at forward bias is much larger
than ,we can use a following relationship for the junction
–
curve:
(1)
Total voltage of the diode in general can be presented
as
(2)
where )is junction voltage;small non-linear
contribution is related to the
photo-induced processes in the diode
chip
and to the
IIC
.If there are no small correction terms
of ,the regular effect at the threshold is the decrease of the differen-tial resistance by
quantity
(3)
That is exactly the junction differential resistance just below
the threshold.If the measured value
is ,the threshold-related step of this value
is
(4)
The photo-induced term in (2)is included to account for phe-nomena of photoresponse of different parts of the diode chip to own radiation that is generated in the active region (sponta-neous or both spontaneous and stimulated).Usually the spon-taneous emission is con fined by the semiconductor chip and mainly lost by internal absorption.The photoelectric absorp-tion can produce photo-EMP at carrier-separating barriers and photoconductivity in absorbing layers.Scattered laser emission is subjected also mainly to the internal absorption.In an opti-mized laser structure,these photo-effects are suppressed:poten-tial barriers other than working p-n junction are not desirable in the chip.It could be observed in early-generation laser diodes,but in modern commercial diodes,the resistance of the diode is minimized which means there are no uncontrollable barriers.As to the photoconductivity,it can be,for example,produced in narrow-bandgap cap layer or sometimes in the substrate if the bandgap there is smaller than the radiation photon energy.We believe that this effect is small as the dark conductivity of narrow-bandgap layers is quite high,as a rule.For example,the cap layer is doped usually to
10
cm or higher.Thus we do not expect any substantial photoconductivity effect.
Another important origin of the voltage correction is the injection-induced yers adjacent to p-n junc-tion are subjected to carrier injection,namely,the optical con finement (waveguide)layers,barriers between QWs if any,and those parts of the cladding layers where the leakage of excess carrier occurs from the waveguide region.These layers are transparent to the emission of QWs,therefore,the photoconductivity seems to be not in effect.On the other hand,waveguides and barriers are usually not doped,so that their initial resistance can be substantial.Characteristic thickness of involved layers
is 10nm or less for QWs and for barriers between them,100–200nm for each waveguide layer,1–
2m for each cladding layer.Thus,most important is the resistance of waveguide layers and,if the carrier leakage occurs,the resistance of claddings may also come into play.There is also the possibility of unintentionally formed depletion layers in the laser heterostructure [15].We call again the layer under
consideration as a sensitive layer.A voltage drop on it
is
,
where is the
current,is the resistance of the layer.Actual drift transport through the layer is in fluenced by injection of excess carriers.This voltage drop decreases along with the
current rise
if decreases more steeply
than
.The decrease
of is stopped by pinning of quasi-Fermi levels in the active region above the laser threshold.This contributes a positive change of differential resistance.
B.Phenomenological Approach to Injection-Induced Conductivity
Assuming that the leakage is negligible at the threshold,we can estimate the contribution of the IIC in the waveguiding re-gions of the laser structure.Assume also that the conductivity of the waveguide regions is controlled by injected carriers with a
density
of
.It is much smaller than the carrier density in QW because carriers are rapidly captured from the waveguide regions to QWs.The total resistance of the waveguide region
is
(5)
12IEEE JOURNAL OF QUANTUM ELECTRONICS,VOL.41,NO.1,JANUARY 2005
where is total thickness of the considered
region,is elec-tron
mobility,is ratio of hole mobility to electron mobility,
and is the area of the active region.The IIC voltage drop
is
and the corresponding contribution to the differ-ential resistance
is
(6)
Below the threshold,this expression gives for the partial IIC differential resistance a negative value if the dependence
of
on is steeper than linear.This is just the case.Remember,
that is the carrier density in the waveguiding region,therefore it is much less than the density in QWs,and it is maintained by pumping and by thermal activation from QWs.For simplicity,
assume
that
is power function of ,
namely (7)
where is a coef ficient
and
is a power exponent.In this
case
(8)
therefore,this value is negative
if .
Consider now what does occur at the laser threshold.Assume
that is strictly saturated above threshold as well as the carrier density in the QWs.In this case,we have at the threshold but below
it
(9)
where subscript th denotes threshold values of variables.Above the threshold the junction differential resistance and
derivative
are assumed both equal to zero,and we have at the
threshold but above
it
(10)
The threshold related step of the differential resistance
is
(11)
This expression contains two terms of opposite signs there-fore,depending on parameters the result can change sign.With assumption of (7)we
obtain
(12)
A criterion of anomalous (positive)sign of the differential resistance step
is
(13)
and
if ,there will be no change of the differ-ential resistance at the threshold.It is also seen from (13)that the anomaly is much more probable at
larger ,but,in prin-ciple,
small does not exclude the anomaly.
In Fig.5curves
of
are shown calculated for a similar model of the laser with
different
as indicated.Other numerical parameters
are meV
,
Fig.5.Calculated value of IdU=dI versus current I for a simpli fied model of laser diode with different values of resistivity R of sensitive layer at the laser threshold fixed at 20mA.An inversion of the sign of the threshold-related kink is
illustrated.
mA.We had put an equilibrium carrier
density
in the sensitive layer in order to avoid large resistance of the layer at small current.Note that we have assumed a constant
value
of
and we only
varied (in case of temperature and pressure variations
both
and are affected).The curve
for
is a regular case with a maximum negative step at the threshold.With increase
of
the step decreases and then changes sign.In frames of this model,the sign inversion occurs
at
smaller
if the power
exponent is larger.The simple power function is taken here in order to obtain analytic results for illustrative purposes.The detailed modeling of the carrier distribution across the separate-con finement heterostructure is rather complicated and is a subject of a number of papers.
There are no analytic expressions
for
.From this modeling,it can be seen that occurrence of the
anomalous sign is more probable if the threshold
value
is larger.On the other hand,to exclude this anomaly one has to provide lower resistance of sensitive layers in the structure.Esti-mation by (5)gives the waveguide layer resistance of
1at fol-lowing
parameters:
cm,
cm
cm
/Vs,
cm .The carrier density in waveguide layer can be in the range 10–
10
cm as it is typically 2–3orders lower than that in active region.Effect of cooling is some freeze-out of the conductivity in undoped and low-doped materials,particularly,in waveguide regions.The anomalous kink is observed at lower temperature whereas at room temperature the same diode behaves in a reg-ular manner.This can be explained by increase of the initial re-sistance of the waveguide region at cooling due to freeze-out of conductivity,according to approach reported earlier in [6],[8].Hardly similar effect in the claddings can in fluence the behavior:the thermal leakage of carriers is reduced at lower temperature.Therefore,the region responsible for the anomaly is the undoped
waveguide.Note that the reduction
of
at lower temperatures should reduce the anomalous term
in
.Hydrostatic pressure leads to the blue shift of laser emission.In GaAs –AlGaAs QW lasers the shift is 9.8meV/kbar in the wavelength range around 780nm [16].There is also an increase of the threshold current (see Fig.4)that is explained tentatively
ELISEEV et al.:ANOMALOUS DIFFERENTIAL RESISTANCE CHANGE AT THE OSCILLATION THRESHOLD IN QUANTUM-WELL LASER DIODES 13
by increase of the carrier leakage from active QWs into wave-guide layers and into cladding layers.The leakage is sensitive to the energy barrier.It is known that under pressure,the energy barrier between direct conduction band -minimum in QW and
indirect -minima in barrier layers decreases with a
rate meV/kbar in GaAs –AlGaAs lasers
and meV/kbar in Al-GaInP-based lasers [16].At the Al content exceeding 0.43in Al-GaAs the lowest minimum in the conduction band occurs at
the point.Therefore under pressure the QW becomes effectively more and more shallow and also
the -barriers in the claddings approach the Fermi level in the well.This leads to an increase of electron leakage
into -minima and thus to the increase
in .Therefore there is one factor in the (13),namely
increasing enhancing the anomalous behavior.Due to increased leakage at high pressure we cannot exclude the contribution of claddings to sensitive layers.Important electrical effect of high hydrostatic pressure is also associated with modi fication of the conductivity of undoped waveguide.Deep levels of defects and residual im-purities can move with pressure with respect to the conduc-tion-band edge,both in direct and indirect AlGaAs.In n-type claddings the deep centers due to Si donors (so-called DX cen-ters)form up to four states that can be metastable at low temper-atures.The effect of pressure
on
in (12)can therefore be complex,entering not only
through but also
through
and .
V .C ONCLUSION
Temperature and hydrostatic pressure effects were investi-gated in AlGaAs laser diodes operating in wavelength ranges between 780and 850nm.Spectral tuning and change of threshold current were measured.Electrical characterization by differential
–curves shows that there are cases of anomalous behavior that is a positive step of the differential resistance at the threshold instead of regular negative step.These anomalous kinks of differential
–curves are identi fied in two typical cases:in some laser diodes the regular behavior at normal cir-cumstances converts into anomalous one under high hydrostatic pressure or under lowered temperature.We suggest that the voltage drop on the sensitive layer in the laser heterostructure produces a small correction to the diode
–curve,so the latter includes additional nonlinear electrical component besides the p-n junction.The differential resistance of the sensitive layer contributes to the threshold-related kink with a sign opposite to the regular effect.Therefore,algebraic summation provides sometime regular (negative)cumulative result,but sometime this summation gives an anomalous (positive result).Occa-sional variations of parameters of the sensitive layers in diodes fabricated by different producers give rise to the observation of the anomaly in some samples.High pressure and low tem-perature are factors favorable for the anomaly as they increase the initial resistance of the sensitive layer (and the threshold currents in case of pressure).The sensitive layers are most probably the undoped optical-con finement (waveguide)layers of the separate-con finement heterostructure.The conductivity of this sensitive layer is modi fied by the injected carriers (effect of the injection-induced conductivity).A similar effect can be expected from photoconductivity effect in other sensitive layers.But in well-designed laser diodes there are no candi-
dates for photo-sensitive layers,as other components of the heterostructure are either transparent to the emission of active region or low-resistance ones to give no rise of competitive voltage contribution.
The voltage correction caused by IIC produces variations of measured differential resistance step associated with details of the laser structure (thickness of sensitive layer,composition and doping level,carrier depletion,etc.).We demonstrated here that low temperature and high pressure are both favorable for anoma-lous behavior.These two factors,temperature and pressure,pro-duce opposite effects on the threshold current in AlGaAs lasers:lowering temperature gives lower threshold,but higher pressure produces higher threshold.But in both cases we noticed the ap-pearance of an electrical anomaly that we associate with injec-tion-induced conductivity.
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14IEEE JOURNAL OF QUANTUM ELECTRONICS,VOL.41,NO.1,JANUARY2005
Peter G.Eliseev(M’87–SM’89)was born in St.Petersburg,U.S.S.R.,in1936. He received the Diploma degree in physics from Moscow State University (MSU),Moscow,Russia,in1959,and the Candidtae and Doctor Sci.degrees from the P.N.Lebedev Physics Institute(FIAN),Russian Academy of Sciences, Moscow,in1965and1974,respectively.
He was with the Physics Department of MSU from1959to1963and since 1963he has been with FIAN.As an Invited Research Professor,he was with Research Center for Advanced Science and Technology,University of Tokyo (1991),the Ferdinand-Braun Institute,Berlin,Germany(1993-1994),Univer-sity of Tokushima,Tokushima,Japan(1998-1999),and University of Nagoya, Nagoya,Japan(1999-2000).Since1995,he has been the Research Professor at the Center for High Technology Materials,University of New Mexico,Albu-querque,on leave from FIAN.The mainfield of his activity is physics and tech-nology of semiconductor lasers.He is the author or coauthor of several books and more than500scientific papers.
Dr.Eliseev was awarded the State Prize of the U.S.S.R.in science and tech-nology(1984)for pioneering development of quaternary heterostructure mate-rials,and is a recipient of the N.Holonyak OSA Award(2004).Since1992, he has been a Correspondent Member of the Russian Academy of Natural Sci-ences.He is a member of OSA.
Pawel Adamiec was born in Nowa Deba,Poland,in1976.He received the M.Sc.degree in physics from Rzeszow University,Rzeszow,Poland,in2000. He is currently working toward the Ph.D.degree at Warsaw University of Tech-nology,Warsaw,Poland.
He performs experiments at the High Pressure Research Center of Polish Academy of Sciences,Warsaw,Poland.He investigates the optical and elec-trical properties of laser diodes as a function of pressure and temperature. Artem Bercha was born in Chernovtsy,Ukraine,in1965.He graduated from Uzhgorod National University,Uzhgorod,Ukraine,in1987.He received the Ph.D.degree from the Institute for Physics of Semiconductors,Kiev,Ukraine, in1994.His major studies were on optical properties of GaAs–AlAs short period superlattices.
From1995to2000,he worked as a Scientific Researcher at the Institute of Physics and Chemistry of Solids and as an Assistant Professor in the Electronic Systems Faculty of Uzhgorod National University.Since2001,he has had a postdoctoral position at the High Pressure Research Center of Polish Academy of Sciences,Warsaw,Poland,and investigates the properties of semiconductor laser diodes under high hydrostatic pressure.Filip Dybala was born in Poland in1975.He received the M.Sc.degree in elec-tronics from Wroclaw University of Technology,Wroclaw,Poland,in2000.He is currently working toward the Ph.D.degree at the Warsaw University of Tech-nology,Warsaw,Poland,and in the High Pressure Research Center of Polish Academy of Sciences,Warsaw.
He investigates the properties of laser diodes under high hydrostatic pressure for wavelength tuning.
Roland Bohdan was born in Mukatchevo,Ukraine,in1965.He graduated from Uzhgorod National University,Uzhgorod,Ukraine in1987,where he made the-oretical research on short-period superlattices.He is currently working toward the Ph.D.degree at the High Pressure Research Center of Polish Academy of Sciences,Warsaw,Poland.
He investigates the properties of visible and infrared laser diodes,in particular blue InGaN–GaN lasers and InGaAsSb lasers.
Witold A.Trzeciakowski was born in1952.He obtained the M.Sc.and Ph.D. degrees in physics from Warsaw University,Warsaw,Poland,in1974and1980, respectively.
From1974to1980,he worked as an Assistant Professor in the Department of Physics,Warsaw University.In1980,he joined the High Pressure Research Center of the Polish Academy of Sciences where he has been working untill now. He obtained the degree of Associate Professor(docent)in1989and the title of Professor in2000.Initially,he worked on semiconductor theory(shallow and deep impurity states,magnetic and electricfield effects,heterostructure elec-tronic states),then he turned to experimental physics(deformation effects in QWs,Raman scattering)and to device physics(the effect of pressure on laser diodes,electrical and optical pressure sensors).He worked as a Scientist with NRC,Ottawa,Canada,University of Florence,Italy,Universities of Bordeaux and Grenoble,France,University of Valencia,Spain,SUNY at Buffalo,and with the Technical University of Athens,Greece.。