Physics of impurity bands and two-dimensional high mobility hole gases in (110) oriented GaAs using Si as an acceptor
F. Fischer
%We report physics of an impurity band in bulk p-type (110) GaAs using Si as a dopant. We have identified the Mott-transition in this system by investigating non-degeneratly and degeneratly doped samples. %We deduce the density and hopping gap of a formed impurity band. %In addition we performed the first growth of a high mobility two-dimensional hole gas (2DHG) in a modulation-doped heterostructure in (110) GaAs:Si by modulating the growth conditions and obtain a hole mobility of %$\mu = 175~000~\textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at a density of $p=2.4\times10^{11}~\textnormal{cm}^{-2}$ for an ungated sample which also shows the expected spin splitting at zero B-field. %We are able to tune the density of the sample with an evaporated Al-gate. %We observe only a weak anisotropy of the mobility for the two principal in-plane directions and a persistent photoconductivity effect unusual for 2DHG samples, with a factor of $\times 2$ increase in density. %This new growth technique is relevant for III-V MBE systems equipped with Si as the only doping source. %We locate the metal-insulator transition in bulk doped p-type (110) GaAs with Si as an acceptor, and we implement the metallic layers as modulation doping in high mobility p-type heterostructures on this facet. In bulk doped systems, we report gap energies for hopping and band conduction in the insulating regime, and experimentally determine the bulk density of the metal-insulator transition. %to be almost an order of magnitude higher than expected, presumably due to autocompensation. %The poor morphology of these p-layers prohibits their use in standard heterostructure growth, %but by modulating the growth conditions, %but if the growth conditions are changed for only the modulation doped layer, %high mobility heterostructures can nonetheless be achieved. We implement metallic layers of Si-doped (110) GaAs as modulation doping in high mobility p-type heterostructures, changing to p-growth conditions for the doping layer alone. The strongly auto-compensated doping is first characterized in bulk samples, identifying the metal-insulator transition density and confirming classic hopping conduction in the insulating regime. To overcome the poor morphology inherent to Si p-type (110) growth, heterostructures are fabricated with only the modulation doping layer grown under p-type conditions. Such heterostructures show a hole mobility of $\mu = 1.75\times10^5~ \textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at density $p=2.4\times10^{11}~ \textnormal{cm}^{-2}$. We identify the zero field spin-splitting characteristic of p-type heterostructures, but observe a remarkably isotropic mobility and a persistent photoconductivity unusual for p-heterojunctions grown using other doping techniques. This new modulated growth technique is particularly relevant for p-type cleaved-edge overgrowth and for III-V growth chambers where Si is the only dopant. %In transport measurements of such a system, we observe a p-type mobility of $\mu = 1.75\times10^5~\textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at $p=2.4\times10^{11}~\textnormal{cm}^{-2}$ density, and identify the spin-splitting characteristic of p-type heterojunctions but observe a remarkably isotropic mobility and a persistent photoconductivity unusual for p-heterojunctions grown using other doping techniques. %This new modulated growth technique is relevant for III-V MBE systems equipped with Si as the only doping source. % Matts abstract total %We report studies of the metal-insulator transition in bulk doped p-type (110) GaAs where Si is used as an acceptor, and we implement the metallic layers as modulation doping in high mobility p-type heterostructures on this facet. In bulk doped systems, we report gap energies for hopping and band conduction in the insulating regime, and experimentally determine the bulk density of the metal-insulator transition to be almost an order of magnitude higher than expected, presumably due to autocompensation. The poor morphology of these p-layers prohibits their use in standard heterostructure growth, but if the growth conditions are changed for only the modulation doped layer, high mobility heterostructures can nonetheless be achieved. %In transport measurements of such a system, we observe a p-type mobility of $\mu = 1.75\times10^5~\textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at $p=2.4\times10^{11}~\textnormal{cm}^{-2}$ density, and identify the spin-splitting characteristic of p-type heterojunctions but observe a remarkably isotropic mobility and a persistent photoconductivity unusual for p-heterojunctions grown using other doping techniques. %This new modulated growth technique is relevant for III-V MBE systems equipped with Si as the only doping source.
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%\begin{frontmatter}


%\title {Physics of impurity bands and two-dimensional high mobility hole gases in (110) oriented GaAs using Si as an acceptor}
%\title{Si as an acceptor in (110) GaAs for high mobility p-type heterostructures}
\title{Modulating the growth conditions:  Si as an acceptor in (110) GaAs for high mobility p-type heterostructures}


\author{F. Fischer}
\author{M. Grayson}
\author{D. Schuh}
\author{M. Bichler}
\author{G. Abstreiter}
\affiliation{Walter Schottky Institut, Technische Universit\"at M\"unchen, 85748, Garching, Germany}
\author{K. Neumaier}
\affiliation{Walther Meissner Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany}


 
%\thanks[ref1]{
%Corresponding author.\\ E-mail: matthew.grayson@wsi.tum.de\\
%Phone: +49-89-289-12778\\
%Fax: +49-89-3206620
%}
 
\begin{abstract}
%We report physics of an impurity band in bulk p-type (110) GaAs using Si as a dopant. We have identified the Mott-transition in this system by investigating non-degeneratly and degeneratly doped samples. 
%We deduce the density and hopping gap of a formed impurity band. 
%In addition we performed the first growth of a high mobility two-dimensional hole gas (2DHG) in a modulation-doped heterostructure in (110) GaAs:Si by modulating the growth conditions and obtain a hole mobility of
%$\mu = 175~000~\textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at a density of $p=2.4\times10^{11}~\textnormal{cm}^{-2}$ for an ungated sample which also shows the expected spin splitting at zero B-field. %We are able to tune the density of the sample with an evaporated Al-gate. 
%We observe only a weak anisotropy of the mobility for the two principal in-plane directions and a persistent photoconductivity effect unusual for 2DHG samples, with a factor of $\times 2$ increase in density. 
%This new growth technique is relevant for III-V MBE systems equipped with Si as the only doping source. 
%We locate the metal-insulator transition in bulk doped p-type (110) GaAs with Si as an acceptor, and we implement the metallic layers as modulation doping in high mobility p-type heterostructures on this facet. In bulk doped systems, we report gap energies for hopping and band conduction in the insulating regime, and experimentally determine the bulk density of the metal-insulator transition. 
%to be almost an order of magnitude higher than expected, presumably due to autocompensation. 
%The poor morphology of these p-layers prohibits their use in standard heterostructure growth, 
%but by modulating the growth conditions, 
%but if the growth conditions are changed for only the modulation doped layer,
%high mobility heterostructures can nonetheless be achieved. 

We implement metallic layers of Si-doped (110) GaAs as modulation doping in high mobility p-type heterostructures, changing to p-growth conditions for the doping layer alone.  
The strongly auto-compensated doping is first characterized in bulk samples, identifying the metal-insulator transition density and confirming classic hopping conduction in the insulating regime.  
To overcome the poor morphology inherent to Si p-type (110) growth, heterostructures are fabricated with only the modulation doping layer grown under p-type conditions.  
Such heterostructures show a hole mobility of $\mu = 1.75\times10^5~ \textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at density $p=2.4\times10^{11}~ \textnormal{cm}^{-2}$.  
We identify the zero field spin-splitting characteristic of p-type heterostructures, but observe a remarkably isotropic mobility and a persistent photoconductivity unusual for p-heterojunctions grown using other doping techniques.  
This new modulated growth technique is particularly relevant for p-type cleaved-edge overgrowth and for III-V growth chambers where Si is the only dopant.

%In transport measurements of such a system, we observe a p-type mobility of $\mu = 1.75\times10^5~\textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at $p=2.4\times10^{11}~\textnormal{cm}^{-2}$ density, and identify the spin-splitting characteristic of p-type heterojunctions but observe a remarkably isotropic mobility and a persistent photoconductivity unusual for p-heterojunctions grown using other doping techniques. 
%This new modulated growth technique is relevant for III-V MBE systems equipped with Si as the only doping source.
% Matts abstract total
%We report studies of the metal-insulator transition in bulk doped p-type (110) GaAs where Si is used as an acceptor, and we implement the metallic layers as modulation doping in high mobility p-type heterostructures on this facet. In bulk doped systems, we report gap energies for hopping and band conduction in the insulating regime, and experimentally determine the bulk density of the metal-insulator transition to be almost an order of magnitude higher than expected, presumably due to autocompensation. The poor morphology of these p-layers prohibits their use in standard heterostructure growth, but if the growth conditions are changed for only the modulation doped layer, high mobility heterostructures can nonetheless be achieved. 
%In transport measurements of such a system, we observe a p-type mobility of $\mu = 1.75\times10^5~\textnormal{cm}^2/\textnormal{V}\textnormal{s}$ at $p=2.4\times10^{11}~\textnormal{cm}^{-2}$ density, and identify the spin-splitting characteristic of p-type heterojunctions but observe a remarkably isotropic mobility and a persistent photoconductivity unusual for p-heterojunctions grown using other doping techniques. 
%This new modulated growth technique is relevant for III-V MBE systems equipped with Si as the only doping source.
\end{abstract}


%\keywords{
%A semiconductors \sep B crystal growth \sep D quantum Hall effect \sep persistent photoconductivity \sep mass anisotropy}
\pacs{81.10.-h}

\maketitle

%\section{Introduction}
	% This new technique invented at the WSI opens new device possibilities for standard III-V growth chambers since both p- and n-type high mobility layers can now be grown on the same substrate using the same standard dopant (Si) as both acceptor and donor, respectively.
%FRANK�S INTRO
%We investigate the metall-insulator transition (MIT) in bulk p-type (110) oriented GaAs which is discussed in the first part of the article and we were, for the first time, able to grow and investigate a two dimensional hole gas (2DHG) in a modulation-doped heterostructure on the (110) GaAs surface using Si as an acceptor by changing the growth conditions for the dopant layer, discussed in the second part of the article. 
%In contrary to a 2DHG the growth of modulation doped high mobility two dimensional electron gases (2DEG) on (110) GaAs is standard with the highest mobilities achieved using Si as a donor dopant \cite{fischer:108}.
%This new technique opens new device possibilities for GaAs based growth chambers since both p- and n-type high mobility two-dimensional layers can be grown on the same $\left(110\right)$ substrate using the same standard dopant (Si) as both acceptor and donor.\\  
%This achievement of high mobility 2DHGs on $\left(110\right)$ GaAs by doping with Si opens various new possibilities for novel studies of interacting carrier systems.
%\indent The valence band structures of GaAs is characterized by with different types of holes and anisotropic, non-parabolic dispersion relations.
%In bulk GaAs crystals the heavy holes (HH) and light holes (LH) are degenerate at the zone center $\Gamma$-point.
%By assuming parabolic dispersion relations one can deduce effective masses for holes, %(see Table \ref{effective_bulk_masses})
%which are about an order of magnitude larger then the mass of electrons in the conduction band of GaAs. The heavy mass of the holes is expected to decrease the required density to observe Wigner crystallisation (WC) in a 2DHG. Evidence for WC and metal insulator transition has been reported in recent years \cite{papadakis:5592}.
%Furthermore holes show a much stronger spin-orbit coupling than electrons leading to a zero-magnetic-field spin-splitting \cite{winkler:1}.\\  
%
%MATT�S INTRO <<
\indent High mobility two-dimensional (2D) holes in GaAs are of research interest both for their strong spin-orbit coupling and for their heavy mass.  
Studies of spin effects may have implications for the field of spintronics, since a large Rashba term splits the spin subbands even at zero external magnetic field, $B$ \cite{ winkler:1}.  
The large mass has lead to studies of a new kind of metal insulator transition and evidence of a Wigner crystal \cite{ papadakis:5592}.\\
%>>
\indent Previously 2D hole gas (2DHG) systems 
%<< or bulk p-type samples >>
have been grown on different facets of GaAs substrates using Be \cite{stormer:685} or C \cite{wieck:51} as an acceptor. Si was used as an acceptor either
on $\left(311\right)\textnormal{A}$ substrate where the highest 2DHG hole mobilities have been achieved. 
%or on the (110) surface limited to bulk p-type growth up to now.
%but which have anisotropic mobility by a factor of 2 \cite{henini:451}.
The disadvantage of Be is that 
%<<
its high vapor pressure and diffusivity causes it to contaminate the growth chamber, and %>>
introducing it into a high mobility III-V growth chamber leads to a general degradation of sample quality.\\
%The disadvantage of Be compared to Si or C is that it is more diffusive and leads to dopant segregation and  introducing it into a high mobility III-V growth chamber would lead to a general degradation of sample quality.\\
%, or on $\left(001\right)$ oriented substrates where Si can be deposited into a metallic layer of Ga and then annealed in an $\textnormal{As}_4$ enviroment \cite{quivy:171}.\\
%The growth of 2DHGs enables research on the properties of holes.
%Holes are interesting because
%in contrast to conduction band electrons there are different types of holes with larger masses which interact and therefore give a rich valenceband structure. In bulk GaAs crystals there is a degeneracy of both heavy holes (HH) and light holes (LH) at the zone center $\Gamma$-point. The HH mass is up to a factor of 12 larger than the GaAs electron mass of $m^* = 0.067 m_e$ and the effective masses of the HH and LH's are highly anisotropic (see Table \ref{effective_bulk_masses}). 
%\begin{table}
%\center
%\begin{tabular}{|c|c|c|}
%\hline
%   & $ \left[ 001 \right] $ & $\left[ 110 \right]$ \\%& $\left[ 111 \right]$ \\
%\hline
%HH & $0.35~m_e$           & $0.65~m_e$     \\      %& $ 0.8 m_e$ \\
%\hline
%LH & $0.09~m_e$           & $0.080~m_e$  \\        %& $0.077m_e$ \\
%\hline
%%SO & \multicolumn{3}{c|}{$0.165 m_e$} \\%
%\hline%
%\end{tabular}
%\label{effective_bulk_masses}
%\caption{Effective masses of heavy holes (HH) and light holes (LH) for different crystal orientations in bulk GaAs \cite{adachi:1}, with $m_e$ being the free electron mass}
%\end{table}
%This results in a smaller Landau-level separation and mobility anisotropies, respectively. 
%In two dimensional hole systems, the quantum confinement lifts the degeneracy of HH and LH at the $\Gamma$-point but also leads to band mixing. With increasing density the HH-like states are occupied first and, up to a certain density, alone responsible for the transport properties  
%In two dimensional hole systems, the transport properties are governed by HH's because quantum confinement lifts the degeneracy of HH and LH at the $\Gamma$-point. Heavy mass systems are of increasing interest because dilute systems are more susceptible to carrier-carrier interactions
%, and the effective interparticle distance rs (in units of the Bohr radius) is proportional to the mass: $r_s \propto n^{-1/2}/a_B \propto m^*$ 
%\cite{shayegan:343}. 
%Thus for a given density $n$, the heavier the mass is, the more relevant the carrier-carrier interactions are. 
%The heavy mass of the holes decreases the required density to observe Wigner crystallisation (WC). 
%Evidence for WC and metal insulator transition has been reported in recent years \cite{papadakis:5592}.
%Furthermore holes show a much stronger spin-orbit coupling than electrons leading to a zero B-field spin-splitting \cite{winkler:1}.\\
%This could possibly be used for realizing electron-hole double layer systems \cite{kane:3266}. 
%\section{Bulk p-type (110) grown GaAs}
%\subsection{Growth of a non-degenerately doped sample}
%The growth was carried out in an EPI GenII high-mobility MBE chamber on $\left(110\right)$ oriented ($\pm0.5^\circ$) 2" epi-ready subtrates. The substrate temperature was monitored by a pyrometer, the $\textnormal{As}_4$-flux was calibrated by an ion gauge and the Ga growth rate by reflection high-energy electron diffraction (RHEED) measurements on a (001) GaAs substrate.
%
%<<
\indent In this Letter, we present a new p-type modulation doping method for (110) GaAs whereby the growth conditions for the Si modulation doping alone are adjusted to induce incorporation as an acceptor.
We first confirm the bulk metal-insulator transition (MIT) under high autocompensation, complemented with a study of the activated hopping in the insulating state, and then we use the metallic layers as modulation doping for a high mobility p-type heterojunction. \\
%>>
\indent We begin with 
% << the discussion >>
studies of the MIT 
% << and present and analyze the experimental results of Hall and resistance measurements of >>
in bulk p-type doped samples. 
To calibrate the Si doping density and efficiency for p-type growth on $\left(110\right)$ GaAs, we grew 
% << a series of >> 
several bulk doped $1~\mu\textnormal{m}$ thick, non-degenerately and degenerately p-doped samples with different doping densities. 
%In the subsequent paragraphs we will have at look at a non-degenerately doped samples 
%grown for acceptor activation energy measurements
%and degenerately doped samples. % used for heterostructure growth.\\  
Si is amphoteric in GaAs 
%\cite{agawa:1171} 
and can act as both donor and acceptor during growth depending on its incorporation on the Ga or As lattice site.
Especially at morphology optimized growth conditions on the $\left(110\right)$ GaAs surface, % <<
labeled Type I % >>
(Table I), Si acts 
% <<
predominantly % >>
as donor.
% and enables growth of high mobility two-dimensional electron gases (2DEG) \cite{fischer:108}.
\begin{table}
\center
\begin{tabular}{|c|c|c|c|c|c|}
\hline
  & & & & $\textnormal{GaAs}$  & \\
  & & \raisebox{1.5ex}[-1.5ex]{$ \textnormal{T}$}  & \raisebox{1.5ex}[-1.5ex]{$\textnormal{P}^{\textnormal{BEP}}_{\textnormal{As}_4}$} & $\textnormal{growth rate}$ & \raisebox{1.5ex}[-1.5ex]{$\textnormal{morphology}$}\\
\hline
I & n-type & $490^\circ\textnormal{C}$           & $6\times10^{-5}~\textnormal{mbar}$          & $0.177~\textnormal{nm}/\textnormal{s}$ & $\textnormal{excellent}$ \\
\hline
II & p-type & $640^\circ\textnormal{C}$           & $1\times10^{-5}~\textnormal{mbar}$          & $0.177~\textnormal{nm}/\textnormal{s}$ & $\textnormal{poor}$ \\
\hline
%SO & \multicolumn{3}{c|}{$0.165 m_e$} \\
%\hline%
\end{tabular}
\label{growth_conditions}
\caption{Growth conditions for n-type (type 1) and p-type (type II) bulk growth}
\end{table}
However, when the substrate temperature is increased and the As pressure lowered,
% <<
labelled Type II %>> 
(Table I), the number of Si-acceptors outweighs the Si-donors leading to a net p-doping.
%incorporated as acceptors is larger than the ones being built in as donors, leading to a net p-doping %\cite{tok:4160}.\\
%\indent 
%To study acceptor activation energies one has to grow a sample with a density which is low enough that the metal-insulator transition did not take place. 
% << REPOSITION FRANK�S GROWTH RELATED SENTENCE HERE
% Unfortunately, 
Growing a thick p-doped layer under such conditions, resulted in a surface covered with large, triangular-shaped defects (Fig. \ref{microscope_surface}a) as observed 
%in 
previously
%publications 
\cite{tok:4160}.\\
% >>
\indent We define the acceptor efficiency $\eta$ as the ratio of Si-acceptors $N_A$ to the total number of incorporated silicon atoms $N_{Si}$ and the compensation ratio $\kappa$ as the ratio of Si-acceptors $N_A$ to Si donors $N_D$. We calibrate assuming a
% <<
Si-acceptor % >>
doping efficiency of $\eta = N_A/N_{Si}=0$ 
% << and a compensation ratio >>
$\left( \kappa = N_A/N_D=0 \right)$ for n-type GaAs on a $\left( 001\right)$ oriented substrate. 
% 
% << REPOSITION FRANK�S METALLIC SPECIFICATIONS SENTENCE HERE
Samples with an acceptor density increased to $N_A=7.1\times10^{18}~\textnormal{cm}^{-3}$ exhibit a metallic behavior down to 4.2 K.
The hole density is $p=2.1\times10^{18}\textnormal{cm}^{-3}$ with $\eta_{4.2K} \approx 0.59$ $\left( \kappa_{4.2K} \approx 1.45 \right)$ for $N_{Si} = 1.2\times10^{19}\textnormal{cm}^{-3}$.
% >>
The low density sample has $p=1.7\times10^{17}\textnormal{cm}^{-3}$ at $300~\textnormal{K}$. %assuming a one carrier system and all acceptors being ionized. 
With $p=N_A-N_D$ at room temperature one deduces $\eta_{300K} \approx 0.55$ 
% << and 
$\left( \kappa_{300K} \approx 1.22 \right)$ % >>
at a Si density of $N_{Si} = 1.7\times10^{18}\textnormal{cm}^{-3}$ at $300~\textnormal{K}$.\\
%For this system we evaluate a doping efficiency of $\eta \approx 0.55$ at a Si density of $N_{Si} = 1.7\times10^{18}\textnormal{cm}^{-3}$.
%\subsection{Analysis}
% <<
\indent Transport in the heavily auto-compensated insulating sample is well-described by hopping conduction in a parallel impurity band. %>>
The temperature dependence of the Hall coefficient of this sample (Fig. \ref{hall_coefficient}) 
% << can be described by
is expected to show the following functional form (following the notation of \cite{ efros:1}): % >>

\begin{displaymath}
R_H(T) \sim \left\{
\begin{array}{ll}
e^{\epsilon_1/kT} & T>50~\textnormal{K} \\
e^{-\epsilon_1/kT} & 25~\textnormal{K}<T< 50~\textnormal{K}  \\
\textnormal{const} &   T< 25~\textnormal{K}
\end{array}
\right.
\end{displaymath}
with the longitudinal resistance (inset Fig. \ref{hall_coefficient})
 $R_{xx}\sim e^{\epsilon_3/kT}$ for $T<28~\textnormal{K}$ and $R_{xx}\sim e^{\epsilon_1/kT}$ for $T>28~\textnormal{K}$.
% << (following the notation of \cite{efros:1}).>> 
This is typical for lightly bulk-doped semiconductors with conduction in the valence band and in an impurity band, with the activated behavior $\epsilon_3= 2.1~\textnormal{meV}$ characterizing the nearest neighbor hopping gap \cite{efros:1}.
%The temperature dependence of this sample shows a non-monotonic activated behavior of the Hall coefficient (Fig. \ref{hall_coefficient}), while the longitudinal resistance at the lowest temperature shows a different activated behavior $R_{xx}\sim e^{-\epsilon_3/kT}$(inset Fig. \ref{hall_coefficient}) with activation energy $\epsilon_3 = 2.1~\textnormal{meV}$ (following the notation of \cite{efros:1}). The activated behavior and the peak in the Hall coefficient are typical for lightly bulk-doped semiconductors \cite{efros:1} with conduction in the valence band and in an impurity band with the activated behavior $\epsilon_3$ characterizing the nearest neighbor hopping gap. 
%The Hall coefficient can be deduced by adding the conductivity tensors of both systems and is given by
%\begin{equation}
%R_H = \frac{R_v \sigma_v^2 + R_h \sigma_h^2}{\left(\sigma_v + \sigma_h\right)^2}~,
%\end{equation}
%where $R_c$, $R_h$ and $\sigma_v$, $\sigma_h$ are the Hall coefficients and conductivities of the valanceband and hoppingband carriers.
The deduced acceptor activation energy $\epsilon_1 = 7.8~\textnormal{meV}$
is about a factor of $\times5$ smaller than the activation energy $\Delta E = 35~\textnormal{meV}$ of isolated Si-acceptors in GaAs obtained by Hall-effect measurements \cite{sze:1}. Taking into account that the activation energy in doped semiconductors decreases according to $\epsilon_1 = \Delta E \left[ 1 - (N_A/N_{crit})^{1/3}\right]\approx 14~\textnormal{meV}$ \cite{schubert:1}, the measured $\epsilon_3$ is lower than the expected one 
% <<
and may be % >>
due to an impurity band strongly broadened towards the valence band.
 %One can deduce the acceptor activation energy $\epsilon_1 = 7.8~\textnormal{meV}$ from the slopes of $R_H$ to the left and the right of the indicated maximum. This is about a factor of $\times5$ smaller than the activation energy $\Delta E = 35~\textnormal{meV}$ of Si acceptors in GaAs obtained by Hall-effect measurements \cite{sze:1}.
% A decrease of $\epsilon_1$ with increasing acceptor concentration has been observed before \cite{hill:1815}  
%is maybe due to an impurity band already strongly broadened towards the valence band. 
From the value of $R_H$ in the saturation regime for low temperatures where the valance band holes are frozen out, one can deduce the number of hopping conductors $p_{N_A}=N_A-N_D=5.2\times10^{17}~\textnormal{cm}^{-3}$ involved in transport,
leading to $\eta_{<25K} \approx 0.65$ 
% <<
$\left( \kappa_{<25K} \approx 1.86 \right)$ 
%for the low temperature analysis. >>
  A discrepancy between $\eta_{<25K}$ and $\eta_{300K}$ has been also observed 
% << in other publications 
previously \cite{arushanov:2653} 
% and the more reliable doping efficiency is given at $T<25~\textnormal{K}$ 
with the former being relevant for low-temperature applications. \\ %>>
%\subsection{Growth of a degenerately doped sample}
%It is remarkable that, although the Si dopant densities of the two samples differ by about one order of magnitude, the doping efficiencies $\eta_{<25K}$ and $\eta_{4.2K}$ are nearly identical.
\begin{figure}
\center
\includegraphics[width=7cm,keepaspectratio]{graphics/hall_coefficient2.EPS}
\caption{Arrhenius plot of Hall coefficient showing a non-monotonic temperature dependence. 
%The arrow indicates the maximum where the conductivity changes from hopping- to band-conduction with %increasing temperature. 
The dotted lines indicate the associated activation energies. Inset: longitundinal resistance exhibits activated behavior}
\label{hall_coefficient}
\end{figure}
%We reached a bulk hole concentration up to $p = 2 \times 10^{18}\textnormal{cm}^{-3}$ under these conditions, a good basis for trying modulation doped heterostructures on $\left(110\right)$ GaAs. 
\begin{figure}
\center
\includegraphics[width=9cm,keepaspectratio]{graphics/surface.eps}
\caption{Microscopic picture of a surface and the corresponding growth protocol of a) a $1~\mu m$ thick p-type layer (left) and b) a 2DHG sample of equivalent thickness using modulated growth conditions(right)}
\label{microscope_surface}
\end{figure}
%\section{Growth modulated 2DHG}
 %To improve the quality of the interface and surface we used the high substrate temperature and low As pressure only during growth of the small, $20\mathring A$ thick, doping layer in $\textnormal{Al}_{0.34}\textnormal{Ga}_{0.66}\textnormal{As}$ which was separated from the GaAs heterointerface by $40~\textnormal{nm}$. 
%The rest of the sample was grown under optimal growth conditions.
\indent Now we can compare the experimental results with the theoretical expectations for the MIT.  
The metal-insulator transition is defined by the Mott criterion $a^*_B N_{crit}^{1/3} \approx 0.25$, with $a_B^*\approx15~\textnormal{\AA}$ the effective Bohr radius and $N_{crit}$ the critical transition density \cite{schubert:1} which can be estimated to $N_{crit} 
% <<
= % >> 
5\times10^{18}~\textnormal{cm}^{-3}$ for acceptors in p-type GaAs. The deduced acceptor concentration $N_A=1.1\times10^{18}~\textnormal{cm}^{-3} < N_{crit}$ 
% << for the sample >>
showing insulating behavior is well below the critical density of the MIT. % << The corresponding effective Bohr radius of $a_B^*=24~\textnormal{\AA}$ is larger than the Bohr radius for the MIT. >>
In 
% << conformance 
agreement % >>
with the theory the density $N_A=7.1\times10^{18}~\textnormal{cm}^{-3} > N_{crit}$ 
% << of the sample >>
showing metallic behavior is above the critical density of the MIT.\\
\indent The rest of the article discusses the two-dimensional hole gas, which was fabricated by using a thin layer of the metallic p-type material as a modulation doping.
To overcome the problem of the poor surface morphology and the consequent bad mobility, we grew the modulation doped heterostructure by using two different growth conditions.
%The structure consisted of a standard superlattice buffer followed by a $0.5~\mu\textnormal{m}$ GaAs buffer layer up to the heterointerface, where a $40~\textnormal{nm}$ $\textnormal{Al}_{0.34}\textnormal{Ga}_{0.66}\textnormal{As}$ spacer 
%separates it from the $2~\textnormal{nm}$ thick doping layer. On top of the doping layer we placed a
%$0.3~\mu\textnormal{m}$ $\textnormal{Al}_{0.34}\textnormal{Ga}_{0.66}\textnormal{As}$ spacer layer, below a $10~\textnormal{nm}$ $\textnormal{GaAs}$ cap layer. 
%Up to the doping layer, we grew with a substrate temperature of $490^\circ \textnormal{C}$ and an As pressure of $P^{BEP}_{\textnormal{As}_4}=6\times10^{-6}~\textnormal{mbar}$. Then, to get p-type doping, we  switched to $P^{BEP}_{\textnormal{As}_4}=1\times10^{-6}~\textnormal{mbar}$ and a substrate temperature of $640^\circ \textnormal{C}$. After the doping layer we went back to the previous growth conditions. 
We used type I growth conditions % << of >>
up to the doping layer. Then we changed to type II for the doping and switched back to type I conditions (Fig. \ref{microscope_surface}b).
This resulted in a very good surface morphology for the 2DHG growth (Fig. \ref{microscope_surface}b), comparable to % << a >>
2DEG heterostructures grown on $\left(110\right)$ GaAs \cite{fischer:108}.\\
%\section{Basic characterization of the 2DHG}
\indent 
%After growth of a 2DHG basic characterization can be made by first contacting the sample and then measuring the sheet resistance, and the longitudinal and transverse resistance in magnetic field, from which the density and mobility of the sample can be deduced.
We studied the sample quality with measurements of the longitudinal and 
%<< transversal 
transverse % >>
resistance with a special focus on the low B-field Shubnikov-de Haas oscillations (SdH).
%Transport measurements were performed in either van der Pauw or Hall bar geometry. 
%and made with a four-terminal ac-measurement at frequencies between  $10 - 30~\textnormal{Hz}$ and excitation currents between $10-200~\textnormal{nA}$. 
%For both types of devices we used InZn as contact material to diffuse it into the sample at temperatures between $380^\circ\textnormal{C}$ and $460^\circ\textnormal{C}$ in a forming gas enviroment. 
%Density dependent transport parameters and anisotropies could be studied by thermally evaporating an Al-gate on top of an L-shaped Hall-bar, of which one branch is directed along the $\left[1\overline{1}0\right]$ direction and the other branch along the $\left[001\right]$ direction.
%\subsection{Analysis}
The highest observed hole mobility is $ \mu = 175~000~\textnormal{cm}^2/\textnormal{Vs}$ at a density of $p_{2D} = 2.4 \times 10^{11} \textnormal{cm}^{-2}$ indicating the excellent quality of the samples despite the doping layer with the poor morphology. An ungated sample shows very well developed quantum Hall plateaus and minima of the longitudinal resistance at $30~\textnormal{mK}$ (Fig. \ref{sample_sdh_data}). In the low B-Field regime one can observe a beating of the SdH (Fig. \ref{sample_sdh_data}) which is known from literature for 2DHGs \cite{stormer:126} 
% << and arises 
to arise % >>
from zero-field spin splitting because of inversion asymmetry \cite{winkler:1}. By plotting $R_{xx}$ against $1/B$ and Fourier transforming it \cite{habib:113311} in the low B-Field region (inset Fig. \ref{sample_sdh_data}) one can directly deduce the density of $p^L_{2D} = 1.4 \times 10^{11} \textnormal{cm}^{-2}$ of the lower spin subband and the density  $p_{2D}^U = 1.0 \times 10^{11} \textnormal{cm}^{-2}$ of the upper subband which add up to the total density evident at high B-fields $p_{2D} = 2.4 \times 10^{11} \textnormal{cm}^{-2}$.
\begin{figure}
\center
\includegraphics[width=8cm,keepaspectratio]{graphics/sample_sdH_hall.EPS}
\caption{Longitudinal and quantum Hall resistance data of 2D holes in (110) GaAs. The inset shows the shows the a Fourier transformation of the longitudinal resistance in the low B-field region.}
\label{sample_sdh_data}
\end{figure}

%\begin{figure}[!h]
%\center
%\includegraphics[width=8cm,keepaspectratio]{graphics/density_vs_gate.EPS}
%\caption{Comparison of the measured 2DHG density versus gate voltage with the density calculated from the capacitor relation $p=V_g(\epsilon_0 \epsilon_{GaAs})/(d_{spacer}e)+p_0$}
%\label{density_vs_gate}
%\end{figure}

%\begin{figure}[!h]
%\center
%\includegraphics[width=8cm,keepaspectratio]{graphics/density_vs_mob_ir.eps}
%\caption{2DHG mobility versus density, tuned by either a gate ($\Box$) or by illumination of an ungated %sample ($\bullet$). Inset: Comparison of the measured 2DHG density versus gate voltage with the density calculated from the capacitor relation $p=V_g(\epsilon_0 \epsilon_{GaAs})/(d_{spacer}e)+p_0$. }
%\label{mobility_vs_density}
%\end{figure}
%Although it can be difficult to achieve leakage free gates on 2DHGs \cite{yacoby:1}, 
%The onset of leakage of an evaporated Al-gate was typically at $-0.9~\textnormal{V}$, thus we were able to vary the density by a factor of 4 between $p_{2D} = 0.5~-~ 2.3 \times 10^{11}~\textnormal{cm}^{-2}$ at $4.2~\textnormal{K}$. The mobility increased only up to 
%$\mu = 125~000~\textnormal{cm}^2/\textnormal{Vs}$ at the highest density in the gated sample, indicating a degradation of mobility due to the presence of the gate.
%\section{Mobility anisotropy}
We studied persistent photoconductivity (PPC) which is a common technique to increase the carrier density in two-dimensional electron systems (2DES) 
% << but 
though % >> 
it is uncommon in 2DHGs \cite{stoermer:139}. 
%In pure Be-doped 2DHGs or Si-doped $\left[311\right]$A 2DHGs one is not able to observe PPC \cite{stoermer:139}, except in samples which are unintentionally carbon doped \cite{Oe:3527} or have an inverted heterointerface \cite{kraak:577}. 
%As one can see in Fig. \ref{mobility_vs_density} 
We find a pronounced PPC effect in our samples.
%We observe a PPC in our Si-doped samples. 
The unilluminated, dark density of the 2DHG at $4.2~\textnormal{K}$ is $p_{2D} = 1.17 \times 10^{11} \textnormal{cm}^{-2}$ with a mobility of 
$ \mu = 28~000~\textnormal{cm}^2/\textnormal{Vs}$. By illuminating a Hall-bar sample with a LED we were able to tune the density up to the maximum density of $p_{2D} = 2.3 \times 10^{11} /\textnormal{cm}^{-2}$ with a mobility 
$\mu = 140~000~\textnormal{cm}^2/\textnormal{Vs}$ at $4.2~\textnormal{K}$.\\
\indent By using an L-shaped Hall-bar we investigate the mobility anisotropy of the two principal in-plane directions
$\left[1\overline{1}0\right]$ and $\left[001\right]$.
A considerable mobility anisotropy has been reported in literature for
2DHGs in GaAs \cite{henini:451}. Up to a factor of 4 anisotropy has been observed in Si-doped $\left(311\right)\textnormal{A}$ systems and different Be-doped facets and is partially due to anisotropic interface roughness scattering \cite{heremans:1980} and the anisotropic effective mass. 
Henini, et al. \cite{henini:446} found that in Be-doped $\left(110\right)$ 2DHGs the mobility along $\left[1\overline{1}0\right]$ is about a factor of 3 larger than the mobility along $\left[001\right]$ at a density of $p_{2D} = 1.79 \times 10^{11} \textnormal{cm}^{-2}$. In contrast, in our samples we observed only a very weak anisotropy 
%with a factor of at most $1.08$ anisotropy at $300~\textnormal{mK}$ and $1.25$ at $15~\textnormal{K}$ (inset Fig. \ref{temp_dep_mob_aniso}), with weaker anisotropies observed depending upon the carrier density $p_{2D}$ and the temperature $T$.
mostly pronounced at low temperatures where it is within 
% <<
a factor of %>> 
$1.1$ to $1.3$. 
% << SHIFT SENTENCES AROUND
Fig. \ref{temp_dep_mob_aniso} shows that the mobility is nearly constant for $T<10~\textnormal{K}$ in both directions and that for $T>10{\textnormal{K}}$, $\mu \sim T^{-5/2}$. 
% NEW SENTENCE HERE
From anisotropies in the bulk mass alone, one would expect a mobility anisotropy of a factor of 0.5, leaving open the possibility that anisotropic roughness may be counteracting the mass anisotropy.\\
%From the bulk values one would expect a mass anisotropy of a factor of 0.5 which suggests that anisotropic scattering plays a dominant role. \\
% >>
%with a maximum at $T=13K$. 
\begin{figure}
\center
\includegraphics[width=8cm,keepaspectratio]{graphics/mob_anisotropy_log.eps}
\caption{Log-log plot of temperature dependent in-plane mobility anisotropy for the $\left[1\overline{1}0\right]$ ($\circ$) and $\left[001\right]$ ($\blacksquare$) direction. 
The two principal power-laws are indicated by the dotted lines. Inset: temperature dependent ratio of the 
two mobilities.}
\label{temp_dep_mob_aniso}
\end{figure}
%It is remarkable that there is a well-defined maximum  
%of the mobility ratio at $15~\textnormal{K}$ which we observed to be independent of the density of the sample (inset fig. \ref{temp_dep_mob_aniso}).\\
%\section{Persistent photoconductivity}
%Despite the fact that there are no DX-centers supposed to exist for holes in GaAs \cite{Oe:3527},
%Persistent photoconductivity (PPC) is the permanent increase of carrier density in a conducting system after illumination is tuned off.
%In Si-doped two dimensional {\it electron} systems in GaAs one usually observes PPC which can be attributed to either deep donors, so called DX-centers or to spatial electron-hole separation (For a review, see \cite{nathan:139}).  
%We propose this may be due to deep acceptor traps, since the change in density is similar to the behavior in 2DEGs, due to DX-centers.
%\indent If we compare the change in density from $p_{2D} = 1.17 \times 10^{11}$ up to $p_{2D} = 2.3 \times 10^{11} /\textnormal{cm}^{-2}$ with the PPC in our 2DEGs of similar density we observe that they also have a similar density without illumination. This analogy in behavior leads us to propose that there is a deep 
%acceptor trap responsible for the PPC we observe. 
%\begin{figure}[!h]
%\center
%\includegraphics[width=7cm,keepaspectratio]{graphics/density_vs_mob_ir.eps}
%\caption{Mobility of the 2DHG versus density for different illuminations}
%\label{mobility_vs_density}
%\end{figure}
%\section{Summary}
\indent In summary we 
% << 
characterized heavily autocompensated Si-doped bulk (110) GaAs, and % >>
observed an insulating impurity band for a non-degenerate % <<ly doped >> 
bulk p-type sample below the MIT, and metallic conduction for a degeneratly doped sample. We were able to grow the first high mobility 2DHG on $\left(110\right)$ oriented GaAs using Si as a dopant. We observed an unusual PPC and a weak anisotropy. \\  
\indent High mobility MBE systems, equipped with Si as the {\it only} dopant source can take advantage of this new technique to grow 2DHGs on $\left(110\right)$ oriented GaAs. Since the $\left[110\right]$ orientation is the natural cleavage plane of GaAs, it should also be possible to grow 2DHGs by cleaved edge overgrowth (CEO) \cite{pfeiffer:1697} without introducing additional dopant sources. This enables new devices like atomically precise hole wires and orthogonal 2D-2D tunnel-junctions, for probing the quantum Hall edges of a 2DHG analogous to previous studies in electron systems \cite{huber:164}. It also permits bipolar n-p heterostructures to be prepared in standard III-V growth chambers.\\
\begin{acknowledgements}
This work was supported financially by Deutsche Forschungsgemeinschaft via Schwerpunktprogramm Quantum-Hall-Systeme
%<<
and in the framework of the COLLECT EC-Research Training Network HPRN-CT-2002-00291. %>>
\end{acknowledgements}

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\end{document}

cond-mat0411728.extracted_bib
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\expandafter\ifx\csname bibnamefont\endcsname\relax
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\expandafter\ifx\csname bibfnamefont\endcsname\relax
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\expandafter\ifx\csname citenamefont\endcsname\relax
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\end{thebibliography}