## 1 Introduction  
Deformation potential theory was originally developed by [PERSON] and [PERSON] [1] to describe the interactions between thermal electrons and acoustic vibrational modes in non-polar crystals. It was initially used to explain the dependence of electrical conductivity on pressure. The theory also predicts a dependence of the energy band gap upon dilation; changes in energy band structure consequently result in changes in carrier concentration. This effect of the deformation potential has been exploited in several applications such as strain transducers [2]. It was soon realized that the deformation potential effect can be inverted to explain the generation of electronic strain \(S^{el}\) by charge carriers in cubic semiconductors [3],  
\[S^{el}=\frac{1}{3}\frac{dE_{g}}{dP}\Delta n \tag{1}\]  
where \(dE_{g}/dP\) is the pressure dependence of the energy gap and \(\Delta n\) is the density of photogenerated electron-hole pairs. Studies of photogenerated electronic strain have been undertaken using modulated laser beams to produce photo-acoustic waves [4] as well as by direct imaging of optically-excited semiconductors in a scanning probe microscope [5]. In some materials the electronic strains can be quite large; for instance [4] found the electronic strain in Silicon irradiated with 514.5 nm laser light was 2.6 times larger than the strain generated by thermal expansion under the same conditions. The deformation potential can be either negative or positive. In crystal Silicon \(S^{el}\) is negative (contractile), whereas in crystal Gallium Arsenide \(S^{el}\) is positive (tensile) [6] and therefore also results in expansion similar to thermal strain. In the past two decades, it has become recognized that the deformation potential often plays a dominant role in the lattice dynamics of semiconductor materials following ultrafast laser excitation [7; 8; 9; 10; 11]. In many of these studies, such as the one presented here, small transient changes in lattice spacing can be resolved by high-resolution synchrotron X-ray diffraction, and the logarithmic range of timescales probed can be exploited along with depth or material sensitivity to disentangle the transport of heat, sound, and charge in bulk or heterostructure crystals. Although both the direction and magnitude of the deformation potential has been calculated and measured in many materials of interest, it is generally assumed that the charge carriers are electron-hole pairs and exist locally in equal concentrations [6]. To the best of our knowledge, the contributions of the individual species (electrons or holes) to electronic strain have never been directly distinguished. As time-resolved X-ray Scattering (TRXS) techniques continue to improve temporal and spatial resolution (e.g., [12; 13]), it will become routine to explore charge transport across heterojunctions. This interest is motivated in part by the desire to control semiconductor properties via strain for optimizing devices, especially optoelectronic devices with large concentrations of photogenerated charge carriers. Therefore, we have performed a time-resolved X-ray diffraction measurement to directly observe the effects of photogenerated electrons alone in crystalline GaAs. As shown in Figure 1, an ultrashort pulse of above-bandgap laser light is absorbed on the surface of an intrinsic (undoped) AlGaAs layer that was epitaxially grown on top of a n-doped GaAs substrate. A cap layer, buffer layer, and ohmic metal contacts were used to ensure that the sample remained highly conductive (50 \(\Omega\) across the entire device) so that the photocarriers could easily move through the AlGaAs layer to the buried \(i\)-\(n\) interface which serves as a potential barrier to holes, but a potential drop to electrons. Electrons will therefore cross the interface into the n-GaAs, and eventually either exit the device through a matched load or recombine in the substrate while leaving the holes behind in the intrinsic AlGaAs.