Practical doping principles
Alex Zunger
Citation: Applied Physics Letters 83, 57 (2003); doi: 10.1063/1.1584074
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APPLIED PHYSICS LETTERS
VOLUME 83, NUMBER 1
7 JULY 2003
Practical doping principles
Alex Zungera)
National Renewable Energy Laboratory, Golden, Colorado 80401
共Received 27 January 2003; accepted 21 April 2003兲
Theoretical investigations of doping of several wide-gap materials suggest a number of rather
general, practical ‘‘doping principles’’ that may help guide experimental strategies for overcoming
doping bottlenecks. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1584074兴
Since the operation of carrier-transporting heterojunction
devices is predicated on ambipolar 共p- and n-type兲 doping,
the failure to successfully dope certain classes of materials is
an important bottleneck for the technological utilization of
these materials in electronic devices. As the band gap of a
material increases 共e.g., Si→GaAs→ZnSe→ZnO) it generally becomes increasingly difficult to dope it in a symmetric
共n and p type兲 fashion. For example, whereas diamond can
be doped p type, its n-type doping is rather difficult;1 conversely, while ZnO2–5 and other main-group oxides6 can be
readily doped n type, their p-type doping is problematic.
Striking doping regularities also appear in compounds belonging to the same chemical class, e.g., ZnTe and AIN are
difficult to dope n type, whereas CdS and GaN can be readily
doped n type;7 CuInSe2 can give n-type conduction whereas
CuGaSe2 can exhibit only p-type conduction.8 Doping
bottlenecks have attracted significant attention by both experimentalists 共see reviews in Refs. 1 and 2兲 and
theorists,4 –17 providing highly detailed studies on individual
cases. Yet, this case-by-case focus has sometimes detracted
from observing general regularities and formulating ‘‘doping
rules.’’ In this work, I attempt to distill from recent theoretical studies of individual hard-to-dope systems4 –17 some
general, practical doping principles, loosely referred to as
doping rules. Although such Pauling-esque rules do not
cover all cases, or identify all exceptions, they might provide
basic design guidelines for systematically navigating in the
complex parameter space of experimental attempts to overcome doping bottlenecks.
I will divide the practical doping rules into those that
emerge from 共i兲 Fermi-level-induced compensation effects
共spontaneous generation of ‘‘killer defects’’兲, 共ii兲 the effects
of adjusting the chemical potentials of the different elements,
and 共iii兲 local bonding effects of the dopant to the lattice.
These effects are encoded in the basic three-term formula
that describes the formation enthalpy of dopant D of charge
state q in host crystal H:
⌬H 共 D,q 兲 共 ␮ ,E F 兲 ⫽qE F ⫹n D 共 ␮ D ⫺ ␮ H 兲 ⫹⌬E b ,
共1兲
where ␮ D and ␮ H are the chemical potentials of the dopants
and host, E F is the electro 共chemical兲 potential 共Fermi energy兲, n D is the number of dopants, ⌬E b ⫽E(host⫹defect)
⫺E(host) is the excess energy of the local chemical bonds
around the dopant, and E is the total energy.
共i兲 Doping rules pertaining to Fermi-level-induced compensation effects. When an electron-producing donor ␣
a兲
Electronic mail: [email protected]
共charge q⬎0) is incorporated into a solid, it donates electrons that join the free-carrier reservoir whose energy is E F ;
thus, as Eq. 共1兲 shows, the total donor formation energy increases linearly with E F . Similarly, formation of electroncapturing acceptors 共charge q⬍0) entails removing q electrons from the Fermi reservoir, thus, the acceptor formation
energy decreases linearly with E F . These trends are depicted
schematically in Fig. 1共a兲. It follows from the linear dependencies on E F that when we deliberately dope a materials
n-type 共via donors兲, thus shifting its E F towards the conduction band, the formation energy of native acceptors, such as
cation vacancies V C⫺ or DX centers would decrease to a point
that such ‘‘electron-killers’’ will form spontaneously. For
example,15 n-type doping of GaAs:Si is limited by the spontaneous formation of VGa , whereas n-type doping of Si:As is
limited16 by the formation of VSi . An extreme example for
the spontaneous formation of cation vacancies in response to
n-type doping is the creation of the ordered-vacancy structure 䊐CuGaGeSe4 when one dopes one of the Ga sites of
chalcopyrite 2CuGaSe2 ⫽Cu2 Ga2 Se4 by germanium.18 In
general, once one reaches the Fermi energy E F , called ‘‘n-
FIG. 1. 共a兲 Schematic depiction of the dependence of the formation enthalpy
of defect ␣ in charge states q⫽⫹, 0 and ⫺ on the Fermi energy. The solid
dots denote the donor 共0/⫹兲 and acceptor 共0/⫺兲 transition energies. 共b兲
Schematic depiction of the formation enthalpy of some intrinsic donors
共anion vacancy V A , cation interstitial C i ) and intrinsic acceptors 共cation
vacancy V C and anion interstitial A i ) on the chemical potential.
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0003-6951/2003/83(1)/57/3/$20.00
57
© 2003 American Institute of Physics
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58
Appl. Phys. Lett., Vol. 83, No. 1, 7 July 2003
Alex Zunger
Rule 1: ‘‘n-type doping is facilitated by materials whose
conduction band minima 共CBM兲 are far from the vacuum
level, i.e., materials with large bulk-intrinsic electron affinities ␹. Conversely, n-type doping tends to be compensated in
materials with small bulk-intrinsic electron affinities.’’ This
rule reflects the difficulty in n-type doping of ZnTe and AlN
共Ref. 7兲 or diamond1 ( ␹ ⬵0), the ease of n-type doping
InAs, ZnO, and CdS 共large ␹兲. This rule further suggests that
lowering the CBM via selective alloying 共e.g., adding nitrogen to III–V’s which leads to huge downwards CBM bow(p)
FIG. 2. The n-type pinning energy ␧ (n)
F and p-type pinning energy ␧ F are
ing兲 will enhance n-type doping.20 Any creative chemical
shown relative to the absolute band edge energies 共from Ref. 19兲 of III–V
modification that lowers the CBM could facilitate n-type
and II–VI semiconductors.
doping.
(n)
Rule 2: ‘‘p-type doping is facilitated by materials whose
type pinning energy’’ E F , at which such killer defect 共e.g.,
VBM
is close to the vacuum level, i.e., small bulk-intrinsic
cation vacancy兲 forms, no further progress in n doping can
ionization
potential ⌽. Conversely, p-type doping tends to be
be made, since the spontaneously generated electron killers
compensated
in materials with large bulk-intrinsic ionization
will negate the deliberately introduced donors. Similarly, deenergies.’’
This
rule reflects the ease of p-type doping of
liberate p doping by acceptors 共shifting E F towards the va(p)
antimonides
and
tellurides 共small ⌽兲, and the difficulty in
lence band兲 will instigate at some point E F called ‘‘p-type
p-type doping of the more electronegative oxides and sulpinning energy’’ the spontaneous formation of native ‘‘hole
phides 共large ⌽兲. The rule suggests that enhanced p-type
killers’’ such as anion vacancy V A⫹ or cation interstitial C ⫹
at
i
doping can be facilitated by alloying an element that leads to
which point p-type doping is defeated. Figure 2 shows the
upward bowing of the VBM. One way to shift the VBM
approximate positions of E F(n) and E F(p) in a number of group
upwards is to add a tetrahedrally bonded 3d element with
III–V and II–VI semiconductors, as obtained from firstactive d states, so that coupling with the anion p band will
principles calculations10 and independently from measured
displace the latter to higher energies. An example is the p
maximal carrier densities.9,11 In this figure the valence band
typeness21 of CuAlO2 as compared with oxides such as MgO
maxima were aligned according to the calculated 共unor ZnO that lack shallow d states and, consequently, have
strained兲 band offsets, collected in Ref. 19 for most comdeeper VBM energies and are difficult to dope p type. Any
pound semiconductors, whereas the band gap values are
creative chemical modification that raises the VBM could
taken from low-temperature experimental data. There is an
facilitate p-type doping.
approximate alignment10 of the pinning levels 共horizontal
Rules 1 and 2 explain why diamond is difficult to dope n
lines兲 within given chemical groups of compounds. The potype1 共␹ only ⬍0.2 eV兲 but it is easier to dope diamond
sitions of the pining levels with respect to the host crystal
p-type 共⌽ as low as ⬃5 eV兲, whereas the other form of
band edges determine dopability. For example, in ZnO or
carbon22 C60 is easy to dope n type 共␹ as big as 2.7 eV兲, but
ZnS the E F(p) level is considerably above the valence band
difficult to dope p type 共⌽ as big as 7.6 eV兲. Also, rules 1
maximum 共VBM兲. Thus, the downwards-moving E F in de(p)
and
2, taken together imply that ambipolar doping requires,
liberate p-type doping will encounter E F before encounterin
general,
a small minimum 共not necessarily optically aling the VBM. At this point the system will generate spontalowed兲
gap,
a well-known result. But these rules clarify that
neous hole-killers 共e.g., Zni or VO) before any significant
the
origin
of
doping asymmetry in different materials dedoping commences. Hence, the difficulty in equilibrium p
(p)
pends
on
␹
and
⌽ separately.
doping of ZnO. In contrast, in tellurides or antimonides E F
The
next
rules
refer to ways of eliminating the particular
is at or below the VBM, so a considerable amount of holes
pinning
centers
共‘‘kill
the killer’’兲.
can be generated before the pinning energy is encountered
Rule
3:
‘‘Since
n-type
doping is inhibited by electronand killer defects form. The relevant doping rules summakillers
such
as
the
cation
vacancy
V C⫺ , this can be overcome
rized in Fig. 3 are as follows.
by designing growth conditions which destabilize cation vacancies 共‘‘kill the killer’’兲, e.g., the use of host cation-rich
growth conditions.’’ Naturally, the extent of attainable host
cation richness is limited by the requirement of not precipitating competing cation phases such as elemental cation metals or cation-dopant compounds. Any other method that discourages formation of cation vacancies will facilitate n-type
doping. This includes passivation of cation vacancies, e.g.,
by hydrogen.13 In general, materials that form cation vacancies readily are difficult to dope n type.
Rule 4: ‘‘Since p-type doping is inhibited by hole killers
such as anion vacancy V A⫹ and cation interstitials C ⫹
i , this
can be overcome by designing growth conditions which destabilize these defects 共⬙kill the killer⬙兲, e.g., the use of host
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anion-rich growth conditions, or agents that form complexes
FIG. 3. Summary of the doping rules. Their number is given in parenthesis.
128.138.65.115 On: Tue, 14 Jul 2015 21:26:57
Appl. Phys. Lett., Vol. 83, No. 1, 7 July 2003
Alex Zunger
59
cancy hole-killers. Thus, all other things being equal, it may
with killer defects, or prevent E F from moving.’’ An example
prove easier to do p-type doping via cation-site substitution
is the use of H during Mg doping12 of GaN: without H,
using anion-rich conditions, whereas n-type doping can be
excessive p-type Mg doping will lead to the spontaneous
done via anion-site substitution using cation-rich conditions.
formation of VN once the Fermi energy moves sufficiently
共iii兲 Doping rules pertaining to local defect bonding eftowards the VBM. But since H acts as a donor, it prevents
fects. Although large concentration of N can now be introthe movement of E F towards the VBM, thus defeats the forduced into ZnO3 , the desired p-type doping is often unstable
mation of the VN killer defect. Subsequently, H is annealed
over time, since the nitrogen bond to Zn is not as stable as
out. This rule suggests, for example, that p-type doping of
the original Zn–O bond 关 ⌬E b ⬎0 in Eq. 共1兲兴. This limitation
oxides can be facilitated by creating internal oxygen precipimight be overcome via ‘‘cluster doping.’’ 14
tates that eliminate oxygen vacancies, e.g., using NO or NO2
3,5
Rule 7: ‘‘The local chemical bonding energy around the
sources for nitrogen-doping of ZnO, or using Li2 O sources
dopant could be enhanced via decorating the dopant by
for Li doping of MgO 共Ref. 23兲.
strongly bonding ligands which do not disrupt the host
共ii兲 Doping rules pertaining to chemical potential effects.
bonds.’’ For example, whereas the four Zn–N bonds formed
In general, the second term of Eq. 共1兲 shows how ⌬H for
when N dopes the O site in ZnO are weak, replacing in
formation of anionic or cationic dopants can be regulated via
otherwise pure ZnO one Zn by Al 共a donor兲 and replacing the
control of the chemical potentials during growth 关Fig. 1共b兲兴.
four oxygen neighbors by four nitrogen atoms 共acceptors兲
This figure illustrates the fact that the enthalpy of forming
creates in total four very strong Al–N bonds around AlZn ,
anion vacancies decreases under host cation-rich conditions,
followed by 12 weak Zn–N bonds around each of the four N
whereas the enthalpy of forming cation vacancies decreases
sites. Since AlN is extremely stable, ⌬E b ⫽4E Al–N
under host anion-rich conditions. Here, ‘‘cation rich’’ means
⫹12E Zn–N⬍0. Such cluster doping ideas with ratio of 4:1
the highest cation chemical potential affordable without prebetween acceptors and donors could facilitate stable local
cipitating the elemental cation metal or other competing
dopant bonding and enhanced solubility.14 Interestingly, this
phases. For a cation-site dopant 共e.g., Mn in GaAs兲, a comcluster-doping is predicted to be more stable than
peting phase could be a compound between the dopant and
‘‘codoping’’ 25 between acceptors and donor 共ratio of 2:1兲.
the host anion 共e.g., MnAs兲. The more stable this competing
The seven practical ‘‘doping rules’’ described here could
phase is, the lower the dopant chemical potential must be to
provide guidelines for creative, yet educated experimentaavoid precipitation.
tions with various doping strategies for difficult-to-dope
Rule 5: ‘‘Anion-substituting dopants will be more
wide-gap materials. They are summarized in Fig. 3.
soluble under host anion poor 共⫽host cation rich兲 growth
conditions.’’ This rule reflects the fact that defects that doThis work was supported by the U.S. D.O.E. through
nate host anions to the chemical reservoir 共e.g., anion vaSC-BES,
Contract No. DEAC36-98-GO10337.
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7
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共2002兲.
8
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⫺
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14
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22
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23
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24
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25
4 this could enhance the formation of hole killer V A . Then,
H. Katayama-Yoshida, T. Nishimatsu, T. Yamamoto, and N. Orita, J.
one is
needs
to defeat
the spontaneous
formation
va13, 8901 共2001兲.
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in the article.
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