diff --git a/fastapi/dependencies/models.py b/fastapi/dependencies/models.py
index 3d3567d03..618957894 100644
--- a/fastapi/dependencies/models.py
+++ b/fastapi/dependencies/models.py
@@ -1,8 +1,10 @@
 from dataclasses import dataclass, field
-from typing import Any, Callable, List, Optional, Sequence, Tuple
+from functools import cached_property
+from typing import Any, Callable, List, Optional, Sequence, Union
 
 from fastapi._compat import ModelField
 from fastapi.security.base import SecurityBase
+from fastapi.types import DependencyCacheKey
 from typing_extensions import Literal
 
 
@@ -32,14 +34,12 @@ class Dependant:
     security_scopes: Optional[List[str]] = None
     use_cache: bool = True
     path: Optional[str] = None
-    scope: Literal["function", "request"] = "request"
-    cache_key: Tuple[Optional[Callable[..., Any]], Tuple[str, ...], str] = field(
-        init=False
-    )
+    scope: Union[Literal["function", "request"], None] = None
 
-    def __post_init__(self) -> None:
-        self.cache_key = (
+    @cached_property
+    def cache_key(self) -> DependencyCacheKey:
+        return (
             self.call,
             tuple(sorted(set(self.security_scopes or []))),
-            self.scope,
+            self.scope or "",
         )
diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 6e808cd19..5b28afc4f 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -60,6 +60,7 @@ from fastapi.logger import logger
 from fastapi.security.base import SecurityBase
 from fastapi.security.oauth2 import OAuth2, SecurityScopes
 from fastapi.security.open_id_connect_url import OpenIdConnect
+from fastapi.types import DependencyCacheKey
 from fastapi.utils import create_model_field, get_path_param_names
 from pydantic import BaseModel
 from pydantic.fields import FieldInfo
@@ -138,14 +139,11 @@ def get_parameterless_sub_dependant(*, depends: params.Depends, path: str) -> De
     )
 
 
-CacheKey = Tuple[Optional[Callable[..., Any]], Tuple[str, ...]]
-
-
 def get_flat_dependant(
     dependant: Dependant,
     *,
     skip_repeats: bool = False,
-    visited: Optional[List[CacheKey]] = None,
+    visited: Optional[List[DependencyCacheKey]] = None,
 ) -> Dependant:
     if visited is None:
         visited = []
@@ -238,7 +236,7 @@ def get_dependant(
     name: Optional[str] = None,
     security_scopes: Optional[List[str]] = None,
     use_cache: bool = True,
-    scope: Literal["function", "request"] = "request",
+    scope: Union[Literal["function", "request"], None] = None,
 ) -> Dependant:
     dependant = Dependant(
         call=call,
@@ -254,7 +252,7 @@ def get_dependant(
     if isinstance(call, SecurityBase):
         use_scopes: List[str] = []
         if isinstance(call, (OAuth2, OpenIdConnect)):
-            use_scopes = security_scopes
+            use_scopes = security_scopes or use_scopes
         security_requirement = SecurityRequirement(
             security_scheme=call, scopes=use_scopes
         )
@@ -581,7 +579,7 @@ class SolvedDependency:
     errors: List[Any]
     background_tasks: Optional[StarletteBackgroundTasks]
     response: Response
-    dependency_cache: Dict[Tuple[Callable[..., Any], Tuple[str]], Any]
+    dependency_cache: Dict[DependencyCacheKey, Any]
 
 
 async def solve_dependencies(
@@ -592,7 +590,7 @@ async def solve_dependencies(
     background_tasks: Optional[StarletteBackgroundTasks] = None,
     response: Optional[Response] = None,
     dependency_overrides_provider: Optional[Any] = None,
-    dependency_cache: Optional[Dict[Tuple[Callable[..., Any], Tuple[str]], Any]] = None,
+    dependency_cache: Optional[Dict[DependencyCacheKey, Any]] = None,
     # TODO: remove this parameter later, no longer used, not removing it yet as some
     # people might be monkey patching this function (although that's not supported)
     async_exit_stack: AsyncExitStack,
@@ -616,9 +614,6 @@ async def solve_dependencies(
         dependency_cache = {}
     for sub_dependant in dependant.dependencies:
         sub_dependant.call = cast(Callable[..., Any], sub_dependant.call)
-        sub_dependant.cache_key = cast(
-            Tuple[Callable[..., Any], Tuple[str]], sub_dependant.cache_key
-        )
         call = sub_dependant.call
         use_sub_dependant = sub_dependant
         if (
diff --git a/fastapi/param_functions.py b/fastapi/param_functions.py
index f2bc98976..6c908bdcd 100644
--- a/fastapi/param_functions.py
+++ b/fastapi/param_functions.py
@@ -2246,7 +2246,7 @@ def Depends(  # noqa: N802
         ),
     ] = True,
     scope: Annotated[
-        Literal["function", "request"],
+        Union[Literal["function", "request"], None],
         Doc(
             """
             Mainly for dependencies with `yield`, define when the dependency function
@@ -2264,7 +2264,7 @@ def Depends(  # noqa: N802
                 function will be executed *around* the **request** and response cycle.
             """
         ),
-    ] = "request",
+    ] = None,
 ) -> Any:
     """
     Declare a FastAPI dependency.
diff --git a/fastapi/params.py b/fastapi/params.py
index 6a37091a3..6a58d5808 100644
--- a/fastapi/params.py
+++ b/fastapi/params.py
@@ -766,7 +766,7 @@ class File(Form):  # type: ignore[misc]
 class Depends:
     dependency: Optional[Callable[..., Any]] = None
     use_cache: bool = True
-    scope: Literal["function", "request"] = "request"
+    scope: Union[Literal["function", "request"], None] = None
 
 
 @dataclass
diff --git a/fastapi/types.py b/fastapi/types.py
index 3205654c7..3f4e81a7c 100644
--- a/fastapi/types.py
+++ b/fastapi/types.py
@@ -1,6 +1,6 @@
 import types
 from enum import Enum
-from typing import Any, Callable, Dict, Set, Type, TypeVar, Union
+from typing import Any, Callable, Dict, Optional, Set, Tuple, Type, TypeVar, Union
 
 from pydantic import BaseModel
 
@@ -8,3 +8,4 @@ DecoratedCallable = TypeVar("DecoratedCallable", bound=Callable[..., Any])
 UnionType = getattr(types, "UnionType", Union)
 ModelNameMap = Dict[Union[Type[BaseModel], Type[Enum]], str]
 IncEx = Union[Set[int], Set[str], Dict[int, Any], Dict[str, Any]]
+DependencyCacheKey = Tuple[Optional[Callable[..., Any]], Tuple[str, ...], str]