ABSTRACT
In the last chapter, we saw that Spin Transistors - whether they are of the “field effect” type, or the “bipolar junction” type - do not really yield significant advantages over their traditional charge based counterparts. Spin transistors are hybrid spin devices where charge still plays the dominant role and spin merely augments the role of charge. Digital information (i.e., binary bit 0 or 1) is ultimately encoded by charge. For example, in the case of the SPINFET, when charge flows through the channel of the transistor causing a source-to-drain current, the device is “on” and could encode the binary bit 1. When no current flows and the device is “off,” the encoded bit could be 0. Switching between logic bits is therefore associated with turning on or off a current, which involves physical motion of charges. This physical motion consumes considerable energy, which is ultimately dissipated as heat. Heat dissipation is an extremely serious issue in electronics since it is the
primary threat to the fabled “Moore’s law.” That “law” is an empirical law which predicts that transistor density on a chip will roughly double every 18 months. Moore’s law has driven the commercial juggernaut that we call the electronics industry, and it is sacrosanct. Anything that threatens this law is a looming catastrophe which must be eliminated. If heat dissipation cannot be reduced dramatically by switching from electronics to spintronics, and thereby perpetuating Moore’s law, then perhaps spintronics has little chance of displacing the silicon juggernaut. Fortunately, spintronics can, in principle, reduce heat dissipation signifi-
cantly. With charge based electronics, there is always a fundamental limitation as far as energy dissipation is concerned. Charge is a scalar quantity, which only has a magnitude. Thus, logic levels can be demarcated solely by a difference in the magnitude of charge, or by the presence and absence of charge. Consequently, to switch from one bit to another, we must change the magnitude of charge in the active region of the device, or move charge around in space. That invariably causes a current (I) flow and an associated I2R dissipation (R is the resistance in the path of the current). This dissipation cannot be avoided. Spin, unlike charge, is not a scalar quantity. It is a pseudo vector, with
to
a fixed magnitude of ~/2, but a variable “polarization”. We can make the polarization “bistable” by placing an electron in a static magnetic field, so that the polarization has only two allowed states – parallel to the field and anti-parallel. No other polarization is an eigenstate. Spin polarization therefore becomes a binary variable. We can encode bits 0 and 1 in these two polarizations. For example, the polarization parallel to the field could encode 1 and the anti-parallel polarization could encode 0, or vice versa. In that case, switching can be accomplished simply by flipping the spin, without causing physical motion of charges, or a current flow. This may result in considerable energy saving. There is still some energy dissipated in flipping the spin, but it is of the order of gµBB, where B is the flux density of the global magnetic field that we need to keep the spin polarization bistable. This could be made arbitrarily small by making B → 0. A smaller B, of course, causes more random bit flips, but bit flip errors can be handled with software or error correcting codes up to a point. In fact, errors occurring with a probability as high as 3% can be handled by the most sophisticated codes that are available today [1]. We will later show that, at any temperature T , gµBB must be kept larger than kT ln(1/p) where p is the error probability (associated with random bit flips) that we can tolerate or handle with error correcting codes. This is true as long as the spins are in equilibrium with their thermal environment [2]. Therefore, a smaller B results in a higher error probability, since p > exp[−gµBB/(kT )]. The point to note here is that we need some minimum energy dissipation gµBB ≥ kT ln(1/p) not because the switching mechanism demands it, but because we have to keep the error probability manageable. Since B is required only to make the spin polarization bistable, we ask: why
does spin polarization have to be bistable in this paradigm? In charge based electronics, logic states are ultimately encoded by voltage or current, which are continuous (not discrete) variables. They are certainly not bistable. So, why does spin polarization have to be discrete and bistable? The answer is that, in charge based electronics, there are voltage or current amplifiers with non-linear transfer characteristics that restore strayed logic levels at circuit nodes to one of two values: 0 and 1. A discussion of this can be found in [3]. There is no equivalent device in spintronics to restore logic levels encoded in spin polarization. Therefore, we must ensure that only two spin polarizations are allowed and intermediate polarizations are not stable (or eigenstates). Hence, the need for bistability.
