Abstract:
A magnetic sensor using efficient injection of spin polarized electrons at room temperature can be fabricated by forming a semiconductor layer sandwiched between ferromagnets and forming δ-doped layers between the semiconductor layer and the ferromagnets. A sensing method applies a magnetic field to be measured to the semiconductor layer and observes the conductivity of the sensor. The sensing techniques can achieve high magneto-sensitivity and very high operating speed, which in turn provides ultra fast and sensitive magnetic sensors.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This patent document is a continuation and claims benefit of the earlier filing date of U.S. patent application Ser. No. 10/284,360, filed Oct. 31, 2002 now U.S. Pat No. 6,809,388, which is hereby incorporated by reference in its entirety. 
   U.S. patent application Ser. No. 10/284,183, entitled “Efficient Spin Injection Into Semiconductors”, which has a common assignee and is hereby incorporated by reference in its entirety, may contain some common disclosure and may relate to the present invention. 

   FIELD OF THE INVENTION 
   This invention relates generally to spintronics. In particular, the invention relates generally to a magnetic sensor, a magnetic read nanohead, based on efficient room temperature injection of spin polarized electrons into semiconductors and rotation of their spin under action of a magnetic field. 
   BACKGROUND OF THE INVENTION 
   Over the past decade a pursuit of solid state ultra fast scaleable devices, such as magnetic sensors of nanosize proportions, based on both the charge and spin of an electron has led to a development of new fields of magnetoelectronics and spintronics. The discovery of giant magnetoresistance (GMR) in magnetic multilayers has quickly led to important applications in storage technology. GMR is a phenomenon where a relatively small change in magnetism results in a large change in the resistance of the devices. 
   The phenomenon of a large tunnel magnetoresistance (TMR) of ferromagnet-insulator-ferromagnet structures is a focus of product development teams in many leading companies. TMR is typically observed in F 1 -I-F 2  structures made of two ferromagnetic layers, F 1  and F 2 , of similar or different materials separated by the insulating thin tunnel barrier  1  with thickness typically ranging between 1.4–2 nm. The tunnel current through the structure may differ significantly depending on whether the magnetic moments are parallel (low resistance) or anti parallel (high resistance). For example, in ferromagnets such as Ni80Fe20, Co—Fe, and the like, resistance may differ by up to 50% at room temperature for parallel (low resistance) versus antiparallel (high resistance) moments on ferromagnetic electrodes. 
   It is worth mentioning recent studies of the giant ballistic magnetoresistance of Ni nanocontacts. Ballistic magnetoresistance is observed in Ni and some other nanowires where the typical cross-section the nanocontacts of the nanowire is a few square nanometers. The transport in this case is through very short constriction and it is believed to be with conservation of electron momentum (ballistic transport). The change in the contact resistance can be close to 10 fold (or about 1000%). 
   All magnetic sensors proposed and developed to present day, including the read heads, are based on variations of magnetic configurations, domain structures, in ferromagnets under externally applied magnetic fields. This mechanism does not ensure operating speed and sensitivity required of ultra fast sensors. 
   Interest has been particularly been keen on the injection of spin-polarized carriers, mainly in the form of spin-polarized electrons into semiconductors. This is large due to relatively large spin-coherence lifetime of electrons in semiconductors, possibilities for use in ultra fast devices. One such device in the works is an ultra fast and sensitive magnetic sensor such as a magnetic read head. 
   The possibility of spin injection from ferromagnetic semiconductors (FMS) into nonmagnetic semiconductors has been demonstrated in a number of recent publications. However, the Curie temperature (the temperature above which a material becomes non-magnetic) of magnetic semiconductors is substantially below room temperature. The low Curie temperature limits possible applications. Room-temperature spin injection from ferromagnets (FM) into semiconductors also has been demonstrated, but it remains a difficult task and the efficiency is very low. The low spin injection efficiency makes it very difficult, if not impossible, to develop an ultra fast magnetic sensor operable at room temperature. 
   SUMMARY OF THE INVENTION 
   According to an embodiment of the present invention, a magnetic sensor includes first and second ferromagnetic layers, a semiconductor layer formed between the first and second ferromagnetic layers, a first δ-doped layer formed between the first ferromagnetic layer and the semiconductor layer, and a second δ-doped layer formed between the second ferromagnetic layer and the semiconductor layer. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Features of the present invention will become known from the following description with reference to the drawings, in which: 
       FIG. 1A  illustrates a density of electronic states (DOS) of ferromagnetic Ni; 
       FIG. 1B  illustrates the density of electronic states (DOS) of ferromagnetic Ni, but at a higher resolution than in  FIG. 1A ; 
       FIG. 2A  illustrates an exemplary magnetic sensor according to an embodiment of the present invention; 
       FIG. 2B  illustrates an exemplary magnetic sensor according to another embodiment of the present invention; 
     FIGS.  3 A 1  and  3 A 2  illustrate an exemplary diagram of the magnetic sensors shown in  FIGS. 2A and 2B  at equilibrium and under bias, wherein the first and second δ-doped layers are both formed by heavily doping portions of the semiconductor layer; 
     FIGS.  3 B 1  and  3 B 2  illustrate an exemplary diagram of the magnetic sensors shown in  FIGS. 2A and 2B  at equilibrium and under bias, wherein the first and second δ-doped layers both have energy band gaps that are less than the energy band gap of the semiconductor layer; 
       FIGS. 4A and 4B  illustrate the embodiments of magnetic sensors shown in  FIGS. 2A and 2B  in operation; 
       FIGS. 5A–5D  illustrate an exemplary method of manufacturing the sensor shown in  FIG. 2A ; and 
       FIGS. 6A–6D  illustrate an exemplary method of manufacturing the sensor shown in  FIG. 2B . 
   

   DETAILED DESCRIPTION 
   For simplicity and illustrative purposes, the principles of the present invention are described by referring mainly to exemplary embodiments thereof. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, the present invention may be practiced without limitation to these specific details. In other instances, well known methods and structure have not been described in detail so as not to unnecessarily obscure the present invention. 
   The density of states (“DOS”) is one of main characteristics of electrons in solid states, in particular, in magnetic materials, such as ferromagnetic Ni, Co, and Fe. DOS is referred to as g(E)dE), which is the number of electrons per unit volume in an energy interval (E,E+dE).  FIG. 1A  illustrates the DOS in ferromagnetic Ni, where arrows indicate the DOS for majority (spin up ↑) and minority (spin down ↓) electrons. Note that the DOS have high peaks for both spin-up and spin-down electrons at certain energy intervals. 
     FIG. 1B  illustrates the density of electronic states (DOS) of ferromagnetic Ni, but at a higher resolution than in  FIG. 1A . The energy origin is chosen at the Fermi level E F , i.e., E=E F =0. As shown, there is a very large difference in the density of states of minority and majority d-electrons at E&gt;0 (states above the Fermi level). The peak in the DOS of minority d-electron states is positioned at E=Δ 0 , which for Ni, Δ 0 ≈0.1 eV. Similar region at E&gt;0 exists in Co and Fe. Note that near E≈Δ 0 , the DOS of the majority d-electrons and DOS of s and p electrons are all negligible when compared the DOS of minority d-electrons. Thus, if electrons are injected from the ferromagnetic material with energies E≈Δ 0 , the electrons would be almost 100% polarized. 
     FIG. 2A  illustrates an exemplary magnetic sensor  200  according to an embodiment of the present invention. As shown, the sensor  200  may include first and second ferromagnetic layers  210  and  230 , respectively, and a semiconductor layer  220  formed therebetween. The sensor  200  may also include first and second δ-doped layers  215  and  225 , which are located between the first ferromagnetic layer  210  and the semiconductor layer  220  and between the semiconductor layer  220  and the second ferromagnetic layer  230 , respectively. The sensor  200  may further include a substrate  240 , preferably a metal, formed below the first ferromagnetic layer  110 . 
   In addition, the sensor  200  may include electrodes  260  and  250  electrically connecting, respectively, to the ferromagnetic layer  230  and the ferromagnetic layer  210  or the metal substrate  240 . The electrodes  260  and  250  are not strictly necessary because the ferromagnetic layers  210  and  230  may directly play the role of electrodes. 
   The first and second ferromagnetic layers  210  and  230  may each be formed from various magnetic materials, preferably Ni, Fe and Co, as well as various magnetic alloys, which may include one or a combination of Fe, Co, Ni. The semiconductor layer  220  may be formed from various semiconductor materials including Si, Ge, GaAs, ZnTe, GaSb, GaP, InAs, CdSe, InP, InSb, CdTe, CdS, ZnS, ZnSe, AlP, AlAs, AlSb and also alloys and combinations of these materials. In general, it is preferred that the semiconductor layer  220  be formed from materials with relatively large time of electron spin relaxation τ S  (as will be shown below) such as GaAs, Ge, ZnSe and ZnCdSe. The semiconductor layer  220  is also preferred to be negatively doped. 
   Donor concentrations N d1 , and N d2  of the first and second δ-doped layer  215  and  225  are preferred to be greater than the donor concentration N, of the semiconductor layer  220 , i.e., N d1 , N d2 &gt;&gt;N s  should hold. In one embodiment, one or both of the first and second δ-doped layers  215  and  225  may be formed by heavily doping of portions of the semiconductor layer  220  with electron rich materials. The magnetic sensor  200  thus formed may be described as having a FM-n + -n-n + -FM structure. Examples of electron rich materials include P, As, and Sb, which are typically used to dope semiconductors Ge and Si, and Ge, Se, Te, Si, Pb and Sn, which are typically used to dope semiconductor GaAs. 
   The inventors have discovered that if the following conditions are satisfied, efficient spin-injection of current from the ferromagnetic layers  210  and  230  into the semiconductor layer  220  may take place at room temperature: 
                             N   d1     ⁢     l     +   1     2       ≈     2   ⁢           ⁢         ɛ   0     ⁢     ɛ   ⁡     (     Δ   -     Δ   0       )           q   2           ,                                       N   d2     ⁢     l     +   2     2       ≈     2   ⁢           ⁢         ɛ   0     ⁢     ɛ   ⁡     (     Δ   -     Δ   0       )           q   2                       (   1   )                           l     +   1       ≤     t   0       =         ℏ   2       2   ⁢       m   *     ⁡     (     Δ   -     Δ   0       )               ,                           l     +   2       ≤     t   0       =         ℏ   2       2   ⁢       m   *     ⁡     (     Δ   -     Δ   0       )                           (   2   )               
where N d1  and N d2  represent donor concentrations of the first and second δ-doped layers  215  and  225 , respectively; l +1  and l +2  represent the thicknesses of the first and second δ-doped layers  215  and  225 , respectively; ε 0  represents the permittivity of free space; ε represents a relative permittivity of the semiconductor layer  220 ; Δ represents a height of the Schottky barrier (as measured from the Fermi level of the ferromagnetic layers  210  and  230 ) on the boundaries between the first ferromagnetic layer  210  and the first δ-doped layer  215  and between the second ferromagnetic layer  230  and the second δ-doped layer  225 ; Δ 0  represents the height of the lower and wider potential barrier in the semiconductor layer  220  (also as measured from Fermi level of the ferromagnetic layers  210  and  230 ); q represents elementary charge; and ℏ is the Planck&#39;s constant. For GaAs semiconductor layer, m*≈07 m 0  where m 0  is the mass of free electron and t 0 ≈1 nm. Similarly for Si, the corresponding values are ≈0.2 m 0  and ≈0.5 nm, respectively.
 
   Under the conditions of Equations (1) and (2), the δ-doped layers  215  and  225  become “transparent” for tunneling electrons. In other words, electrons with energy E≧Δ 0  may easily traverse the δ-doped layers  215  and  225 . 
   As noted above, when the barrier height Δ 0  corresponds to the peak in the DOS for minority d ↓ electrons in the ferromagnetic layers  210  and  230  (see  FIGS. 1A and 1B ), the electrons are almost 100% polarized. In other words, P 1  and P 2  are both almost unity, where P 1  and P 2  represent degrees of polarization of injected electrons from the first ferromagnetic layer  210  to the semiconductor layer  220 , the first FM-S interface, and from the second ferromagnetic layer  230  to the semiconductor layer  220 , the second FM-S interface, respectively. It is preferred that the condition of Equation (1) is satisfied to the extent that a dispersion of Δ 0  is equal to the width of the peak in DOS shown in  FIGS. 1A and 1B . Typically, this occurs if Equation (1) is accurate within 20 percent. 
   In another embodiment, one or both of the first and second δ-doped layers  215  and  225  may be formed by growing a n + -doped epitaxial layer on one or both sides of the n-doped semiconductor layer 220 (this structure may also be referred as a FM-n + -n-n + -FM heterostructure). It is preferred that the epitaxially grown δ-doped layers  215  and  225  be doped heavily as practicable and be as thin as practicable. Preferably, one or both of the first and second δ-doped layers  215  and  225  have a narrower energy band gap than the energy band gap of the semiconductor layer  220 , i.e., E gδ1 &lt;E g  and E gδ2 &lt;E g  and at that electron affinities of the δ-doped layers  215  and  225  be greater than an electron affinity of the semiconductor layer  220  by a value close to Δ 0 . 
   If one or both of the first and second δ-doped layers  215  and  225  are formed by epitaxial growth of a very thin heavily doped (i.e., n +  doped) and narrower energy band gap semiconductor layer, the parameters of the layers  215  and  225 , i.e., their respective donor concentrations N d1  and N d2  and their thicknesses l +1  and l +2  should satisfy the following conditions for efficient spin injection: 
                           N   d1     &gt;     2   ⁢           ⁢         ɛ   0     ⁢     ɛ   ⁡     (     Δ   -     Δ   0       )             q   2     ⁢     l     +   1     2             ,                                     N   d2     &gt;     2   ⁢           ⁢         ɛ   0     ⁢     ɛ   ⁡     (     Δ   -     Δ   0       )             q   2     ⁢     l     +   2     2                         (   3   )                 l   +1   ≦t   0   , l   +2   ≦t   0   (4) 
   Examples of such heterostructures include FM 1 —GaAs—Ga 1−x Al x As—GaAs—FM 2  (i.e., n + -δ-doped layers are formed from GaAs and n-doped semiconductor layer is formed from Ga 1−x Al x As), FM 1 —Ge x Si 1−x —Si—Ge x Si 1−x —FM 2 , and FM 1 —Zn 1−x Cd x Se—FM 2 , where x and 1−x quantities refer to the composition of the respective materials. Regarding the n + -δ-doped layers (e.g., GaAs, Ge x Si 1−x  and Zn 1−x Cd x Se), their thickness l +1  and l +2  should be sufficiently thin such that corresponding FM-S interfaces become transparent for electron tunneling. The conditions of Equations (3) and (4) may be satisfied, for example, if the δ-doped layers  215  and  225  are such that the thickness l +1,2 ≦1 nm and the donor concentration N d1,2   + ≧10 20  cm −3 . 
   It is possible that one of the first and second δ-doped layers  215  and  225  are formed from heavily doping a portion of the semiconductor layer  220  and the other of the first and second δ-doped layers  215  and  225  be formed by epitaxial growth. 
   The substrate  240  may be formed preferably from metals such as Ta, Cu, Ag, Au, and P 1 . In addition, the electrodes  250  and  260  may be formed from highly conductive materials such as metals, doped silicon, and doped polysilicon. 
     FIG. 2B  illustrates an exemplary magnetic sensor  200 - 2  according to another embodiment of the present invention. The sensor  200 - 2  is similar to the sensor  200  shown in  FIG. 2A . The sensor  200 - 2  differs from the sensor  200  in that first and second antiferromagnetic layers  270  and  280  may be present. As shown in  FIG. 2B , the first antiferromagnetic layers  270  may be placed between the first ferromagnetic layer  210  and electrode  250  and may play the role of the substrate. Similarly, the second antiferromagnetic layer  280  may be placed between the second ferromagnetic layer  230  and electrode  260 . The antiferromagnetic layers  270  and  280  fix more rigidly magnetizations M 1  and M 2  within ferromagnetic layers  210  and  230 , respectively. The first and second antiferromagnetic layers  270  and  280  may be formed from various materials including FeMn, IrMn, NiO, MnPt (L 1   0 ), α-Fe 2 O 3 , and combinations therefrom. 
   FIGS.  3 A 1  and  3 A 2  illustrate an exemplary diagram of the magnetic sensor  200 ,  200 - 2  along the line II—II shown in  FIGS. 2A and 2B  at equilibrium (FIG.  3 A 1 ) and under bias (FIG.  3 A 2 ), wherein the first and second δ-doped layers  215  and  225  are both formed by heavily doping portions of the semiconductor layer  220 . 
   FIGS.  3 B 1  and  3 B 2  illustrate an exemplary diagram of the magnetic sensor  200 ,  200 - 2  along the line IV—IV shown in  FIGS. 2A and 2B  at equilibrium (FIG.  3 B 1 ) and under bias (FIG.  3 B 2 ), wherein the first and second δ-doped layers  215  and  225  both have energy band gaps that are less than the energy band gap of the semiconductor layer  220 . 
   With references to FIGS.  3 A 1 – 3 B 2 , the operation of the magnetic sensors  200 ,  200 - 2  will be explained. First, under bias at room temperature, spin-polarized electrons from the first ferromagnetic layer  210  are injected into the semiconductor layer  220  through the first δ-doped layer  215  using the concept of efficient room temperature injection described above (see also below). 
   A potential Schottky barrier for electrons always forms at the boundary of any metal-semiconductor interface, such as at the boundary between the first ferromagnetic layer  210  and the first δ-doped layer  215 . If the donor concentration N d1  is sufficiently high and the thickness l +1  is sufficiently small, the first δ-doped layer  215  is “transparent” for tunneling electrons, and the electrons from the first ferromagnetic layer  210  may easily traverse the first δ-doped layer  215 . 
   The electrons that tunnel through the first δ-doped layer  215  meet another lower and wider potential barrier formed in the semiconductor layer  220 . It is preferred that the width d of the semiconductor layer  220  be wide enough. When this occurs, electrons with energies below the barrier height are effectively filtered, and essentially, only the electrons with energies above the barrier height Δ 0  will be able to traverse the semiconductor layer  220 . 
   It is preferred that the height of the barrier in the semiconductor layer  220  is approximately equal to E F +Δ 0  where E F  is the Fermi level at equilibrium. Note that the potential barrier in the semiconductor layer  220  may be manipulated to a desired value by controlling the characteristics of the magnetic sensor  200 ,  200 - 2 , for example by controlling the donor concentration N, of the semiconductor layer  220 . As previously noted, the DOS of minority d ↓ electrons of a ferromagnet reaches maximum at energy level E≈E F +Δ 0  (see  FIGS. 1A and 1B ). For simplicity, origin is chosen such that E F =0. Then the maximum DOS of minority d ↓ electrons exceeds, by more than an order of magnitude, the DOS of other type electrons (s ↑, s ↓, p ↑, p ↓ and d ↑) in the first ferromagnetic layer  210  at E≈Δ 0 . 
   Thus, if the potential barrier height of the semiconductor layer  220  is such that it coincides with Δ 0  then the electrons from the first ferromagnetic layer  210  tunneling through the first δ-doped layer  215  and traverse the length d of the semiconductor layer  220  will be composed of almost all minority d ↓ electrons. In other words, the injected current will be almost completely spin-polarized. 
   Further, the Δ   height of the barrier is preferred to be substantially maintained throughout the width d of the semiconductor layer  220  at equilibrium (see FIGS.  3 A 1  and  3 B 1 ). The height of the barrier may be substantially maintained if the donor concentration N s  and the width d of the semiconductor layer  220  substantially satisfy the following conditions: 
                   N   s     ≤     2   ⁢           ⁢         ɛ   0     ⁢   ɛ   ⁢           ⁢     Δ   0           q   2     ⁢     d   2                   (   5   )                 d   &gt;     d   min       =         a   B     ⁡     (     1       k   B     ⁢   T       )       ⁢           m   0     ⁢     E   B     ⁢     Δ   0         m   e   *                   (   6   )               
where α B =0.05 nm and E B =13.6 eV are the Bohr parameters; m 0  is mass of free electron; T is the sensor temperature and k B  is the Boltzmann constant. For example, d min ≈6 nm for GaAs and d min ≈3 nm for Ge when Δ 0 =0.1 eV and T=300K. Under these circumstances, if d&gt;10 nm and N s ≦10 7  cm −3  the conditions specified by Equations (5) and (6) would be satisfied.
 
   Due to the peculiarity of the DOS in the ferromagnet, the end result is that practically only the minority d ↓ electrons are injected from the first ferromagnetic layer  210  into the semiconductor layer  220 . In other words, the degree of spin polarization P 1  of the injected electrons from the first ferromagnetic layer  210  into the semiconductor layer  220  is close to 1 (or close to unity). The same is true of the degree of spin polarization P 2  of electrons injected from the second ferromagnetic layer  230  into the semiconductor layer  220 . 
   It is preferred that the electrons conserve their spin orientation during transit through the semiconductor layer  220 , i.e., spin ballistic transport is desired. For spin ballistic transport to occur, a transit time τ d  of the electrons through of the semiconductor layer  220  of the width d should be substantially equal to or less than the spin-coherence time τ S  of the electrons in the semiconductor layer  220 . 
   The transit time τ d  is determined by the diffusion and the drift of the electrons under the electrical field Ē inside the semiconductor layer  220  and is equal to τ d =d/v d  where v d =μ n Ē+D n /d , μ n  and D n  are the mobility and the diffusion constant of the electrons. Thus, spin ballistic transport occurs when:
 
 d&lt;d   max   =√{square root over (D     n     τ     S     )}   (7)
 
   According to Equations (6) and (7), the width d of the semiconductor layer  220  should satisfy the following condition: 
                   d   min     =             a   B     ⁡     (     1       k   B     ⁢   T       )       ⁢           m   0     ⁢     E   B     ⁢     Δ   0         m   e   *           &lt;   d   &lt;     d   max       =         D   n     ⁢     τ   S                   (   8   )               
For typical parameters of Ge and GaAs, d min ≈10 −6  cm and d max ≈3×10 −3  cm.
 
   In comparison with earlier proposed magnetic sensors, the sensors  200 ,  200 - 2  shown in  FIGS. 2A and 2B  possess an additional degree of freedom resulting from spin rotation of the injected spin-polarized electrons under the action of an external magnetic field during transit through the semiconductor layer  220  in the spin ballistic transport, τ d ≦τ S . 
   The electron spin rotation occurs with frequency ω=γH where γ=1.76×10 7 Oe −1 s −1  is the gyromagnetic ratio and H is the magnetic field component normal to the spin (see FIG.  3 A 2 ). Thus, the angle of the spin rotation is θH=γHτ d  and its maximum is θ Hmax =γHτ S . Therefore, the total angle θ between the electron spin σ and the magnetization M 2  of the second ferromagnetic layer  230  is θ=θ 0 +θH where θ 0  is the angle between the magnetizations M 1  and M 2  of the first and second ferromagnetic layers  210  and  230 . The theoretical calculations and experimental studies show that the longest values for spin-coherence time τ S  can be realized in negative doped semiconductors (n-semiconductors) and can reach up to 1 ns in ZnSe and GaAs at room temperature. Hence it follows that θ=π can be obtained at H in several hundred Oersteds. 
   A conductivity G of the second FM-S interface, i.e., between the second ferromagnetic layer  230  and the semiconductor layer  220 , change with the angle θ between the electron spin a and the magnetization M 2  of the second ferromagnetic layer  230 . Note that the magnetic sensor  200 - 2  as shown in  FIG. 2B  has an advantage in that antiferromagnetic layers  270  and  280  may be used to fix magnetizations M 1  and M 2  of the first and second ferromagnetic layers  210  and  230 , respectively. The conductivity G of the structures shown in  FIGS. 2A and 2B  may be written as:
 
 G=G   0 (1 +P   1   P   2 cosθ)  (9)
 
where P 1  and P 2  are degrees of polarizations first and second FM-S interfaces as described previously. It was also described above that the variation of the angle θ between the electron spin σ and the magnetization M 2  inside the second ferromagnetic layer  230  can exceed π when the magnetic field is several hundred Oersteds. Thus, the maximum magnetoresistance variation can reach:
 
   
     
       
         
           
             
               
                 
                   
                     G 
                     max 
                   
                   
                     G 
                     min 
                   
                 
                 = 
                 
                   
                     1 
                     + 
                     
                       
                         P 
                         1 
                       
                       ⁢ 
                       
                         P 
                         2 
                       
                     
                   
                   
                     1 
                     - 
                     
                       
                         P 
                         1 
                       
                       ⁢ 
                       
                         P 
                         2 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 10 
                 ) 
               
             
           
         
       
     
   
   As mentioned above, P 1  and P 2  for the sensors  200  and  200 - 2  shown in  FIGS. 2A and 2B  are nearly unity. Therefore, the variation of resistance of the magnetic sensor  200 ,  200 - 2  can reach several orders of magnitude. In other words, the magnetic sensors  200 ,  200 - 2  may be extremely sensitive. 
     FIGS. 4A and 4B  illustrate the embodiments of magnetic sensors  200  and  200 - 2  in operation. As shown, injection of spin-polarized electrons occurs from the first ferromagnetic layer  210  into the semiconductor layer  220 . The electron spin is rotated under action of a magnetic field and it causes change in resistance of the second ferromagnetic layer  230 , which is measured. 
   The magnetic sensors  200  and  200 - 2  may be ultra fast. It was noted above that the transit time τ d  is essentially less than or equal to the spin-coherence time τ S  of the electrons. It was also noted above that for n-doped semiconductor  220  the spin-coherence time τ S  can be less than or equal to 1 ns. This means that the transit time τ d &lt;τ S &lt;1 ns. In other words, the effect of spin injection from the first ferromagnetic layer  210  and the spin rotation may manifest as a change in the resistance in the second ferromagnetic layer in less than 1 ns (or less than a billionth of a second). It should be noted that 1 ns is the maximum time at room temperature. Typically, τ S =0.1–0.01 ns. 
     FIGS. 5A–5D  illustrate an exemplary method of manufacturing the sensor  200  shown in  FIG. 2A . As shown in  FIG. 5A , the substrate  240  may be formed. The substrate  240  may be planarized. Then the first magnetic layer  210  may be formed on the substrate  240 . Material to form the first magnetic layer  210  may be deposited, sputtered, fired on the substrate  240 . The first magnetic layer  210  may also be planarized. 
   Then as shown in  FIG. 5B , the first and second δ-doped layers  215  and  225  and the semiconductor layer  220  may be formed. In one embodiment, the first δ-doped layer  215  may be formed by epitaxial or molecular growth. The first δ-doped layer  215  may also be deposited, sputtered, or fired onto the first magnetic layer  215 . Then the semiconductor layer  220  may be deposited, fired, or sputtered onto the first δ-doped layer  215 . Then the second δ-doped layer  225  may be formed by epitaxial or molecular growth, or may be deposited, sputtered, or fired onto the semiconductor layer. Note that each of the first and second δ-doped layers  215  and  225  and the semiconductor layer  220  may be planarized. Also, the first and second δ-doped layers  215  and  225  may be doped more heavily as compared to the semiconductor layer  220 . 
   In another embodiment, the semiconductor layer  220  may be formed on the first ferromagnetic layer  210  and the first and second δ-doped layers  215  and  225  may be formed by heavily doping appropriate portions of the semiconductor  220 . 
   Then as shown in  FIG. 5C , the second ferromagnetic layer  230  may be formed, again by epitaxial growth, or may be deposited, sputtered, or fired onto on the second δ-doped layer  225 . The second magnetic layer  230  may be planarized. 
   Then as shown in  FIG. 5D , the first and second electrodes  250  and  260  may be formed by sputtering, firing, or depositing materials on the first and second ferromagnetic layers  210  and  230 , respectively. 
     FIGS. 6A–6D  illustrate an exemplary method of manufacturing the sensor  200 - 2  shown in  FIG. 2B . The method to manufacture sensor  200 - 2  is similar to the method illustrated in  FIGS. 5A–5D . Thus the details need not be repeated. However, the methods do differ in first and second antiferromagnetic layers  270  and  270  are formed and the substrate  240  is not. 
   What has been described and illustrated herein are preferred embodiments of the invention along with some of its variations. The terms, descriptions, and figures used herein are set forth by way of illustration only and are not meant as limitations. Many variations are possible within the spirit and scope of the invention, which is intended to be defined by the following claims—and their equivalents—in which all terms are meant in their broadest reasonable sense unless otherwise indicated.